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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q. 342 (page 964)

In the following exercise, $f (x) = 3 x^{2} - 6 x - 1$ ,
Part (a): rewrite the function in $f (x) = a {(x - h)}^{2} + k$ form.
Part (b): graph it by using transformations.

Short Answer

Expert verified

Part (a): The required function is $f (x) = 3 {(x - 1)}^{2} - 4$ .

Part (b): The required graph is given below,

Step by step solution

01

Part (a) Step 1. Given information.

Consider the given function,

$f (x) = 3 x^{2} - 6 x - 1$

Rewrite the function in $f (x) = a {(x - h)}^{2} + k$ form by completing the square,

$f (x) = 3 (x^{2} - 2 x) - 1 f (x) = 3 (x^{2} - 2 x + 1) - 1 - 3 f (x) = 3 {(x - 1)}^{2} - 4$

02

Part (b) Step 1. Graph the function using transformation.

Identify the constants,

$a = 3, h = 1, k = - 4$

Consider the function $f (x) = x^{2}$ .

Multiply y-values by localid="1645117185745" $3$ ,

localid="1645117189379" $f (x) = 3 x^{2}$

Shift right localid="1645117214868" $1$ unit,

localid="1645117221834" $f (x) = 3 {(x - 1)}^{2}$

Shift down localid="1645117224529" $4$ units,

localid="1645117229014" $f (x) = 3 {(x - 1)}^{2} - 4$

Plot the graph,

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