Chapter 11: Q. 517 (page 1069)

In the following exercises, write the function in $f (x) = a {(x - h)}^{2} + k$ form:

Short Answer

Expert verified

The equation is $f (x) = {(x + 1)}^{2} - 5$ .

Step by step solution

Step 1. Given information.

We have given the graph

Step 2. Find the function using vertex form.

Notice that the graph have a vertex of $(- 1, - 5)$ and passes through $(- 2, - 4)$ and $(0, - 4)$ .

The vertex form is given by:

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

For $(- 1, - 5)$ :

$y = a {(x - (- 1))}^{2} + (- 5) y = a {(x + 1)}^{2} - 5$

Note the graph passes through the point $(0, - 4)$ . So, substitute $x = 0$ and $y = - 4 :$

localid="1667913442019" $- 4 = a {(0 + 1)}^{2} - 5 a = 1$

Substitute $a = 1$ in vertex form:

$f (x) = 1 {(x + 1)}^{2} - 5 f (x) = {(x + 1)}^{2} - 5$

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In the following exercises, write the function in $f (x) = a {(x - h)}^{2} + k$ form:

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the function using vertex form.

One App. One Place for Learning.

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In the following exercises, write the function in fx=ax-h2+kform:

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the function using vertex form.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Decision Maths

Geometry

Applied Mathematics

Probability and Statistics

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Study anywhere. Anytime. Across all devices.

In the following exercises, write the function in $f (x) = a {(x - h)}^{2} + k$ form: