Chapter 11: Q. 9.126 (page 1069)

Write the quadratic function in form $f (x) = a {(x - h)}^{2} + k$ whose graph is shown.

Short Answer

Expert verified

The equation of quadratic function shown in the given graph is :

$f (x) = {(x + 3)}^{2} - 1$

Step by step solution

Step 1. Given information.

The vertex of the given graph is $(- 3, - 1)$ .They-intercept is $(0, 8))$

Step 2. Substitute the vertex

Since it is quadratic, we start with the

$f (x) = a {(x - h)}^{2} + k____(1)$

And we know that $(h, k)$ is the vertex.

So, substituting the $h = - 3 k = - 1$ in the equation (1), we get:

$f (x) = a (x - (- 3))^{2} - 1 f (x) = a {(x + 3)}^{2} - 1____(2)$

Step 3. Find the value of a

The y-intercept is $(0, 8)$

Substituting $x = 0 f (x) = 8$ in equation (2), we get:

localid="1664210862662" $f (x) = a {(x + 3)}^{2} - 1 8 = a {(0 + 3)}^{2} - 1 8 + 1 = 9 a 9 a = 9 a = 1$

Step 4. Find the equation of the parabola

Substituting the value $a = 1$ in the equation (2), we get:

$f (x) = {(x + 3)}^{2} - 1$

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Write the quadratic function in form $f (x) = a {(x - h)}^{2} + k$ whose graph is shown.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Substitute the vertex

Step 3. Find the value of a

Step 4. Find the equation of the parabola

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Write the quadratic function in form f(x)=a(x−h)2+kwhose graph is shown.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Substitute the vertex

Step 3. Find the value of a

Step 4. Find the equation of the parabola

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

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Study anywhere. Anytime. Across all devices.

Write the quadratic function in form $f (x) = a {(x - h)}^{2} + k$ whose graph is shown.