Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q. 9.125 (page 961)

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

Short Answer

Expert verified

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

$f (x) = {(x - 3)}^{2} - 4$

Step by step solution

Step 1. Given information.

The vertex of the given graph is $(3, - 4)$

They-intercept is $(0, 5)$ .

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 $h = 3 k = - 4$ in the equation (1), we get:

role="math" localid="1645347026030" $f (x) = a {(x - 3)}^{2} - 4___(2)$

Step 3. Find the value of a

The y-intercept is $(0, 5)$ .

Substituting role="math" localid="1645347054141" $x = 0 f (x) = 5$ in the equation (2), we get:

$f (x) = a {(x - 3)}^{2} - 4 5 = a {(0 - 3)}^{2} - 4 5 = 9 a - 4 9 a = 9 a = 1$

Step 4. Find the equation of the parabola

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

$f (x) = {(x - 3)}^{2} - 4$

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91影视

Write the quadratic function in $f (x) = a {(x 鈭� h)}^{2} + k$ form 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

One App. One Place for Learning.

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91影视

Write the quadratic function inf(x)=a(x鈭�h)2+kform 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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

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Study anywhere. Anytime. Across all devices.

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