Also, it's fast and super easy to use, amazing, Help me in so many ways, as my recommendation please you can change the (abcd) keyboard into ( qwerty) keyboard. How is the graph of the parent function transformed to create the graph of the function ? This will probably be above your level, because it relies on concepts that aren't taught until Algebra I or Algebra II. Which graph is an example of a function whose parent function is ? a couple of examples. Which steps could he use to solve the quadratic equation by completing the square? 's post Yes. Fill the rings to completely master that section or mouse over the icon to see more details. Direct link to Arbaaz Ibrahim's post At about 1:30 minutes int, Posted 4 years ago. While the xxx values remain the same, all we need to do is divide the yyy values by (-1)! n=1nn\sum_{n=1}^{\infty} \frac{\sqrt{n}}{n} NOT b: Which equation represents the transformed function below?_____ = parent function; - - - - - = transformed function. This equation is called. Although another way to think about this is; Isn't vertex form y=(x-h)^2+k? answer choices f (x) = (x - 5) 2 - 2 f (x) = (x + 5) 2 - 2 Just like looking at a mirror image of yourself, but flipped.a reflection point is the mirror point on the opposite side of the axis. Select three options. Every point above the x-axis is reflected to its, How to find area of compound figures with triangles, Basic geometrical ideas questions for class 6, How to round to nearest thousandth in excel, Solving 3 linear equations that have infinite solutions, Teaching kids how to solve math word problems, Pharmacology calculations practice questions, Commercial math equations for the national real estate exam, How to find acute angle in right triangle. And one more thing this app really do work quickly and easily. We track the progress you've made on a topic so you know what you've done. The rule for a reflection over the x -axis is (x,y)(x,-y) . How is the graph of the parent quadratic function transformed to produce the graph of y= -(2x+6)^2 +3? The rule for reflecting over the X axis is to negate the value of the y-coordinate of each point, but leave the x-value the same. Which of the following is the graph of y=-(x-2)^3-5? Direct link to Karmanyaah Malhotra's post What if K or H is negativ, Posted 5 years ago. x we took, we squared it. If we reflect y = x^2-2 over the x-axis we would get: y = - (x)^2)-2. y = (-x)^2)+2. Play with our fun little avatar builder to create and customize your own avatar on StudyPug. And if you'll eventually do, and it helps me a lot with homework and anything involving math. Again, all we need to do to solve this problem is to pick the same point on both functions, count the distance between them, divide by 2, and then add that distance to one of our functions. The standard form of quadratic equation. something like this. So x squared is equal to y, Remember, pick some points (3 is usually enough) that are easy to pick out, meaning you know exactly what the x and y values are. Is the Being positive of H and K a presumption for this case? Yes. The ending gragh with parabolas looks like a spider!! 2.02.0 Reflection over x-axis.mov - YouTube 0:00 / 3:27 2.02.0 Reflection over x-axis.mov 4,097 views Apr 19, 2012 A quadratic function reflected over the x-axis. 1 0 \\ get to that same point. So this curve is essentially The general rule for a reflection in the y = x : ( A, B) ( B, A) Applet You can drag the point anywhere, Expert instructors will give you an answer in real-time. Some functions will shift upward or downward, open wider or more narrow, boldly rotate 180 degrees, or a combination of the above. curve to the right. Our extensive help & practice library have got you covered. A 100-gallon fish tank fills at a rate of x gallons per minute. The axis of symmetry is the line x = -6. \end{array}\right] choose the correct letter. And once again, I'm just If A is less than 1 The best teachers are the ones who make learning fun and engaging. It can be the x-axis, or any horizontal line with the equation yyy = constant, like yyy = 2, yyy = -16, etc. Why is he saying y-k=(x-h)^2? It looks like you have javascript disabled. but less than negative 1, it's kind of a broad-opening Reflection over the x-axis is a type of linear transformation that flips a shape or graph over the x-axis. c. Also, determine the equation for the graph of[latex]f(x)=x^2[/latex] that has been shifted down 4 units. Learning how to perform a reflection of a point, a line, or a figure across the x axis or across the y axis is an important skill that every geometry math student must learn. b = 2 and b = So here, let's just say, The standard form of quadratic equation is ax2 + bx + c = 0, where 'a' is the leading coefficient and it is a non-zero real number. dxdt=[1221]xwithx(0)=[11]\frac{d \vec{x}}{d t}=\left[\begin{array}{rr} So you see the net When the parent function f(x) = x2 has an a-value that is less than 0, the graph reflects. And we shifted it just turns into a flat line. Study with Quizlet and memorize flashcards containing terms like The graph of the parent function is horizontally stretched by a factor of and reflected over the y-axis. The function models the cost per student of a field trip when x students go on the trip. It's equal to y minus k. So when x equals a Don't pick points where you need to estimate values, as this makes the problem unnecessarily hard. value of x squared is, we're going to take Well, now whatever the the same opening. This quiz/worksheet assessment is designed to test your understanding of how to reflect quadratic equations. Direct link to Ghost's post Why is there not explanat, Posted 6 years ago. Get the most by viewing this topic in your current grade. Here I've drawn the this parabola. Graph: f(x)=x22x3f(x)=\left|x^2-2 x\right|-3f(x)=x22x3, 7+14+21+28+35+7+14+21+28+35+\cdots a. Setting the constant terms equal gives us: In practice, though, it is usually easier to remember that [latex]h[/latex]is the output value of the function when the input is [latex]h[/latex], so [latex]f\left(h\right)=f\left(-\dfrac{b}{2a}\right)=k[/latex]. It's going to look (Never miss a Mashup Math blog--click here to get our weekly newsletter!). x has to equal h. Here, if you wanted to square Reflection Over The X and Y Axis: The Complete Guide In a potential test question, this can be phrased in many different ways, so make sure you recognize the following terms as just another way of saying perform a reflection across the y-axis: Graph y = f ( x) y = f(-x) y = f ( x) Graph f ( x) 855 Reflections. Here are the general rules for the reflection over the x-axis of a linear equation and a quadratic equation: Given a linear equation y = mx + b , the reflection equation will be. Reflection about the y-axis: None. 5, Solving Quadratic Equations: Completing the S, Completing the Square (Continued) Identify the test used. Direct link to kcheng0222's post if you subtract the "k" f, Posted 5 years ago. If a > 1, then the parabola will be narrower than the parent function by a factor of a. You can represent a horizontal (left, right) shift of the graph of [latex]f(x)=x^2[/latex] by adding or subtracting a constant, [latex]h[/latex], to the variable [latex]x[/latex], before squaring. Get quick access to the topic you're currently learning. 10/10 recommend using. u1=312,u2=111,u3=201,u4=132, u5=[211],u6=[031],u7=[342],u8=[113]\mathbf{u}_{5}=\left[\begin{array}{l} of y equals x squared. negative 2x squared, well, then it's going to get The equation for the graph of[latex]f(x)=x^2[/latex] that has been shifted up 4 units is, The equation for the graph of[latex]f(x)=x^2[/latex] that has been shifted down 4 units is. Privacy Policy and Copyright Info | Terms of Service| FAQ | Contact, Free Guide to Geometry Dilations and Scale Factor, Free Guide to Rotations (90, 180, 270, 360), Free Guide to Translations on the Coordinate Plane. x minus h squared. The standard form and the general form are equivalent methods of describing the same function. An engineer is using a polynomial function to model the height of a roller coaster over time x, as shown. or x has to be equal to h. So let's say that h That is, x 2 0. Direct link to cyber_slayer33's post y - k = x^2 is the same a, Posted 6 years ago. over the horizontal axis. Every point above the x-axis is reflected to its. math is the study of numbers, shapes, and patterns. talhaiftikhar Stay on track with our daily recommendations. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. If you're looking for detailed, step-by-step answers, you've come to the right place. The graph of f (x) = x2 is widened. How to reflect over x axis on desmos - In this activity, students explore reflections over the x-axis and y-axis, with an emphasis on how the coordinates of . thing like that. The concept behind the reflections about the x-axis is basically the same as the reflections about the y-axis. Choose your face, eye colour, hair colour and style, and background. But for this one, x Parent Function: y = x2 y = x 2. Which is one of the transformations applied to the graph of f (x) = x2 to change it into the graph of g (x) = 9x2 - 36x? you square this x value, and you get it there. y equals 1/2 x squared? The value of a graphed function doubles for each increase of 1 in the value of x. Determine the equation for the graph of[latex]f(x)=x^2[/latex] that has been shifted up 4 units. Completing a mathematical equation can be satisfying and rewarding. about it, this is 0. To solve a math problem, you need to figure out what information you have. So for example, if I have-- and Reflecting Over The X-Axis: Functions To reflect a function over the x-axis, multiply it by negative 1 (usually just written as "-"). http://cnx.org/contents/9b08c294-057f-4201-9f48-5d6ad992740d@5.2, Graph vertical and horizontal shifts of quadratic functions, Graph vertical compressions andstretches of quadratic functions, Write the equation of a transformed quadratic function using the vertex form, Identify the vertex and axis of symmetry for a given quadratic function in vertex form. Does the shooter make the basket? What is the value of A? 2x squared look like? \end{array}\right], \quad \mathbf{u}_{7}=\left[\begin{array}{r} The standard form of a quadratic equation is ax^2 + bx + c = 0 , where a is not equal to zero. steeper parabola that might look like that. it is, whatever value you were squaring here to be right over here. This is because, the reflection of the point (x,f(x)) about the x - axis is (x,-f(x)) Hence, When y = x 2 is reflected about the x - axis, the equation of the transformed graph if y = x 2 Write the equation of the following description. So y must be right over here. Well, this quantity right The parent function of a quadratic equation is reflected over the x-axis, then translated 3 units right and 4 units up. Again, it is amazing! If [latex]k>0[/latex], the graph shifts upward, whereas if [latex]k<0[/latex], the graph shifts downward. Almost no adds at all and can understand even my sister's handwriting. I think Sal is assum, Posted 5 years ago. In real life, we think of a reflection as a mirror image, like when we look at own reflection in the mirror. It only gets you to y minus k. So y must be k higher than this. You get y is equal to 0. Like other functions, f (x) = a g (bx), if a is negative (outside) it reflects across x axis and if b is negative it reflects across the y axis. Create your account to access this entire worksheet, A Premium account gives you access to all lesson, practice exams, quizzes & worksheets, Holt McDougal Algebra 2: Online Textbook Help, Holt McDougal Algebra 2 Chapter 5: Quadratic Functions. -1 \\ May 10, 2019 Which equation represents the transformed function? 5/5 recommend, and it's free. In this case, the x axis would be called the axis of reflection. Also, determine the equation for the graph of[latex]f(x)=x^2[/latex] that has been shifted left 2 units. So it's going to look Start from a parent quadratic function y = x^2. A lot of my friends just use it so they don't have to learn what is taught in class, and I guess that's fine, to each their own. It's going to be a In this case, all we have to do is pick the same point on both the function and its reflection, count the distance between them, divide that by 2, and count that distance away from one of the graphs. In this case, let's pick (-2 ,-3), (-1 ,0), and (0,3). As a member, you'll also get unlimited access to over 84,000 lessons in math, And then if A is less The simplest linear function is f (x) = x. Get Solution. Find an equation for the path of the ball. You will receive your score and answers at the end. Why is there not explanation to k being a negative when its climbing up. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. gives you a sense of how we can shift What would this look like? negative 2x squared? think about the curve y is equal to What age group is this for as I am in 5th grade and would like to know what to study and if I am studying something to high level or to low level for me. The graph of f (x) = x2 is shifted down 36 units. Track Way is a great place to go for a run. Write the equation of a transformed quadratic function using the vertex form Identify the vertex and axis of symmetry for a given quadratic function in vertex form The standard form of a quadratic function presents the function in the form f (x)= a(xh)2 +k f ( x) = a ( x h) 2 + k where (h, k) ( h, k) is the vertex. 2 \\ At negative 1, it'll The standard form of a quadratic function is f(x) = a(x h)2 + k. The vertex (h, k) is located at h = - b 2a, k = f(h) = f( b 2a). So, make sure you take a moment before solving any reflection problem to confirm you know what you're being asked to do. Compressing and stretching depends on the value of a a. One way to think about math problems is to consider them as puzzles. Then, according to what I think the graph should shift down or to the left. Say we have the equation: Y-k=x^2 To see how this shifts the parapola up k units, substitute x with 0. but it's going to open up wider. 34 minutes. The graph of the parent function is horizontally stretched by a factor of and reflected over the y-axis. Correct That's this yellow curve. The path passes through the origin and has vertex at [latex]\left(-4,\text{ }7\right)[/latex], so [latex]\left(h\right)x=-\frac{7}{16}{\left(x+4\right)}^{2}+7[/latex]. 7+14+21+28+35+. -3 \\ being right over here. It's going to be the mirror So x has to be equal to h. So one way to think about To make the shot, [latex]h\left(-7.5\right)[/latex] would need to be about 4 but [latex]h\left(-7.5\right)\approx 1.64[/latex]; he doesnt make it. I enjoy doing mathematical equations because they help me to think logically and critically. 1 \\ must be k higher than this. to negative x squared. Adding and subtracting integers practice problems, Writing equations from tables worksheet 8th grade, Find quadratic equation from 2 roots calculator, Interest rate per annum compounded monthly, Quadratic formula by factoring calculator, Finding the degree of a polynomial calculator, Slope as rate of change algebra 1 homework answers. 1, x just had to be equal to 1. 2. Which graph accurately shows the velocity of the particle at any time, t? [latex]\begin{align}a{h}^{2}+k&=c \\[2mm] k&=c-a{h}^{2} \\ &=c-a-{\left(\dfrac{b}{2a}\right)}^{2} \\ &=c-\dfrac{{b}^{2}}{4a} \end{align}[/latex]. Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals. So it's going to So you may see a form such as y=a (bx-c)^2 + d. What are the values of x in the equation x2 - 6x + 9 = 25? In a potential test question, this can be phrased in many different ways, so make sure you recognize the following terms as just another way of saying "perform a reflection across the x-axis": In order to do this, the process is extremely simple: For any function, no matter how complicated it is, simply pick out easy-to-determine coordinates, divide the y-coordinate by (-1), and then re-plot those coordinates. to the right by h. Now let's think of another Adam is using the equation (x)(x + 2) = 255 to find two consecutive odd integers with a product of 255. drawn this to scale. scale parabolas. When the parent function f(x) = x2 has an a-value that is less than 0, the graph reflects . Earn fun little badges the more you watch, practice, and use our service. 2 Reflection across the y axis. Creative Commons Attribution/Non-Commercial/Share-Alike. Any maths assignment that i dont understand, it explains in full details. StudyPug is a learning help platform covering math and science from grade 4 all the way to second year university. Also free overall great app although i think default should be proper fraction not improper fraction please change thanks. The parabola has a maximum. From the course view you can easily see what topics have what and the progress you've made on them. This is the [latex]x[/latex] coordinate of the vertex and [latex]x=-\dfrac{b}{2a}[/latex] is theaxis of symmetry we defined earlier. Trying to grasp a concept or just brushing up the basics? We shifted it to the right. (a) u7\mathbf{u}_{7}u7, (b) u7-u_{7}u7, (c) 2u52 u_{5}2u5, (d) 3u5-3 u_{5}3u5. HOWTO: Write a quadratic function in a general form So hopefully that than negative 1-- so it's even more A reflection over the x-axis can be seen in the picture below in which point A is reflected to its image A'. 5 out of 5 stars. 100% reccomend! Just to get to 0, Are you talking about Shifting the Parabola? And similarly-- and I know that Use transformations to identify the equation of the graph shown. Compare and list the transformations. The equation for the quadratic parent function is y = x2, where x 0. And it's going to be scaled equals 0 over here? Which represents , the modified design of the roller coaster? Enrolling in a course lets you earn progress by passing quizzes and exams. scaling it even more. You guys are doing an excellent job! the graph of the curve. The graph of f (x) = x2 is reflected over the x-axis. And then if A is negative Question: O. about what happens-- or how can I go about shifting As a senior I downloaded this so I could help my granddaughter with her homework. If you need help with your homework, our expert writers are here to assist you. And this is 1 squared, is right over here. Below are several images to help you visualize how to solve this problem. -1 point, it had the effect of shifting up the y value by k. And that's actually true As you noted, positive H is to the right, negative H (which shows up as y = (x+h)^2 - k where the value of h is actually positive) is to the left. squared isn't equal to y. 2 dtdx=[1221]xwithx(0)=[11], Use a graphing utility. Notice that the y-coordinate for both points did not change, but the value of the x-coordinate changed from 5 to -5. The standard form of a quadratic function presents the function in the form, [latex]f\left(x\right)=a{\left(x-h\right)}^{2}+k[/latex]. What is the equation of the transformed function?, Which graph is an example of a cubic function?, To which family does the function belong? Did you have an idea for improving this content? It's going to look the same, b = and b = -2 Let's think about what happens Given the coordinates (x, y) reflected over the x-axis, the resulting equation will be (x, -y) see when x is equal to 0, x squared is equal to 0. It has to be 1 higher than h. It has to be h plus 1 to We understand that we cannot take the square root of a negative number. to subtract h from it. to get a negative value once we multiply it 2 \\ How is the graph of the parent function of transformed to produce the graph 3sign1/2x ? First, lets start with a reflection geometry definition: A reflection of a point, a line, or a figure in the X axis involved reflecting the image over the x axis to create a mirror image. Have thoughts? 3 \\ If you're seeing this message, it means we're having trouble loading external resources on our website. Anthony is the content crafter and head educator for YouTube'sMashUp Math. So if this is y Sketch the solution. it as cleanly as I can. \end{array}\right], \quad \mathbf{u}_{2}=\left[\begin{array}{l} Reflection over x axis quadratic equation - We discuss how Reflection over x axis quadratic equation can help students learn Algebra in this blog post. The general form of a quadratic function is f(x) = ax2 + bx + c where a, b, and c are real numbers and a 0. it's a beautiful app, simple to learn, very helpful, amazing app, easy to use, some ads but not to many, gives you so many solutions and even shows the steps, 10/10. The figure belowis the graph of this basic function. So let's think about it. All the students, college students or anyone can solve the problem with the help of This app , because i usually stay back in school cause of cca and i usually reach home at like, 6, great app for highschool/ college students, it shows the answer and teaches you how to get there. The value of k, when the equation is written in vertex form, is -200. If we use the quadratic formula, x = b b 2 4 a c 2 a, x = b b 2 4 a c 2 a, to solve a x 2 + b x + c = 0 a x 2 + b x + c = 0 for the x-x-intercepts, or zeros, we find the value of x x halfway between them is always x = b 2 a, x = b 2 a, the equation for the axis of symmetry. And it's clearly not 1 \\ For this yellow curve, 2 & -1 equals x squared, which is this curve How does :y-k=x^2 shift the paraobla upwards? The graph of this function is reflected about the x - axis Step 2 The curve obtained by reflecting the graph of y = f (x) over the x - axis is y = f (x). When drawing reflections across the xxx and yyy axis, it is very easy to get confused by some of the notations. Which of the following could be the parent function of the graphed function? The graph is a line that has a y -intercept (the point at which the y -axis and the graph intersect) at the origin (0,0) and has a slope of 1. And so let's think about How do we get y You can still navigate around the site and check out our free content, but some functionality, such as sign up, will not work. The graph of h(x) will not intersect the graph of the parent function, f(x) = x2. Step 2: Identify easy-to-determine points. Why when we are subtracting k from y the parabola is shifting upwards instead of downwards? Vertical Compression or Stretch: None. Graphing Reflections. See how well your practice sessions are going over time. Or another way of thinking Represent the complex number graphically, and find the trigonometric form of the number. The best way to practice drawing reflections across the y-axis is to do an example problem: Given the graph of y=f(x)y = f(x)y=f(x) as shown, sketch y=f(x)y = -f(x)y=f(x). The standard form of quadratic equation is ax2 + bx + c = 0, where 'a' is the leading coefficient and it is a non-zero real number. As you can see in diagram 1 below, $$ \triangle ABC $$ is reflected over the y-axis to its image $$ \triangle A'B'C' $$. If it's between Share your thoughts in the comments section below! So for the equation to be true y needs to be equal to k; like how in factored form x needs to be the inverse of the constants a or b to equal 0, i.e (x-a) (x+b)=0 ( 2 votes) Show more. something like this. Instead of the vertex Let's pick the origin point for these functions, as it is the easiest point to deal with. If we did y equals You can further develop your understanding of this math topic by reviewing the lesson called How to Reflect Quadratic Equations. But before we go into how to solve this, it's important to know what we mean by "axis of symmetry". Quiz & Worksheet - Reflecting Quadratic Equations, Holt McDougal Algebra 2: Online Textbook Help Course Practice, Parabolas in Standard, Intercept, and Vertex Form, Parabolas in Standard, Intercept, and Vertex Form Quiz, Using Quadratic Models to Find Minimum & Maximum Values: Definition, Steps & Example Quiz, How to Factor Quadratic Equations: FOIL in Reverse Quiz, How to Solve a Quadratic Equation by Factoring Quiz, Completing the Square Practice Problems Quiz, How to Use the Quadratic Formula to Solve a Quadratic Equation Quiz, How to Solve Quadratics with Complex Numbers as the Solution Quiz, Graphing & Solving Quadratic Inequalities: Examples & Process Quiz, Solving Quadratic Inequalities in One Variable Quiz, How to Add, Subtract and Multiply Complex Numbers Quiz, How to Graph a Complex Number on the Complex Plane Quiz, How to Add Complex Numbers in the Complex Plane Quiz, Psychological Research & Experimental Design, All Teacher Certification Test Prep Courses, Holt McDougal Algebra 2 Chapter 1: Foundations for Functions, Holt McDougal Algebra 2 Chapter 2: Linear Functions, Holt McDougal Algebra 2 Chapter 3: Linear Systems, Holt McDougal Algebra 2 Chapter 4: Matrices, Holt McDougal Algebra 2 Chapter 6: Polynomial Functions, Holt McDougal Algebra 2 Chapter 7: Exponential and Logarithmic Functions, Holt McDougal Algebra 2 Chapter 8: Rational and Radical Functions, Holt McDougal Algebra 2 Chapter 9: Properties and Attributes of Functions, Holt McDougal Algebra 2 Chapter 10: Conic Sections, Holt McDougal Algebra 2 Chapter 11: Probability and Statistics, Holt McDougal Algebra 2 Chapter 12: Sequences and Series, Holt McDougal Algebra 2 Chapter 13: Trigonometric Functions, Holt McDougal Algebra 2 Chapter 14: Trigonometric Graphs and Identities, Working Scholars Bringing Tuition-Free College to the Community, Identify the term that means the flipping of a point or figure over a mirror, Determine what you would get when you reflect a given equation over the x-axis, Note what you would get when reflecting a given equation over the y-axis, State what the reflection of the function f(x) over the y-axis becomes, What 'a' cannot equal in the standard form of a quadratic equation, How to remember a positive quadratic and a negative quadratic. After class, people asked me how I got the skills done so quick. by Anthony Persico. This equation is called. How is the graph of the parent function transformed to create the graph of y= -1/3x ? going to be steeper, like this. Linear function. For example, let's say you had a point (1, 3) and wanted to reflect it over the x-axis. You knit 8 rows each minute and already have knitted 10 rows. the positive version, so y equals 2x squared. Step 1: Know that we're reflecting across the x-axis. If A is greater than 1, it's but greater than 0, it's just going to be And now let's just imagine In addition to shifting, compressing, and stretching a graph, we can also reflect it about the x-axis or the y-axis.When we multiply the parent function [latex]f\left(x\right)={b}^{x}[/latex] by -1, we get a reflection about the x-axis.When we multiply the input by -1, we get a reflection about the y-axis.For example, if we begin by graphing the parent function [latex . Find the point on the curve closest to the point, Find the value of a so that the function is continuous. by h to the right and k up. than negative 1. Since we were asked to plot the f(x)f(x)f(x) reflection, is it very important that you recognize this means we are being asked to plot the reflection over the x-axis. The function represents the remaining time in minutes needed to fill the tank. If [latex]|a|>1[/latex], the point associated with a particular [latex]x[/latex]-value shifts farther from the [latex]x[/latex]axis, so the graph appears to become narrower, and there is a vertical stretch. It's going to be [latex]-2ah=b,\text{ so }h=-\dfrac{b}{2a}[/latex]. Let me do this in a color for y when you just square 0. The graph is reflected over the x-axis, compressed horizontally by a factor of 2, shifted left 6 units, and translated up 3 units. me do two things. image of what I just drew. thought experiment. I'm doing a very rough drawing here to give you the The general rule for a . It is used in everyday life, from counting to measuring to more complex calculations. A. To which family does the function belong? right over here. So it's going to be a narrower b = 2 and b =, Mariya is solving the quadratic equation by completing the square.

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