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Chapter 4: Q. 107 (page 195)

G(x)=(x+3)2(x-2)

(a) Identify the x-intercept of the graph of G

(b) What are the x-intercepts of the graph ofy=G(x+3)

Short Answer

Expert verified

(a) x-intercepts of G(x)are -3,2

(b) x-intercepts ofG(x+3)are-1,-6

Step by step solution

01

Part (a) Step 1.  Solve for x

Set y=0in the given function and solve for x

localid="1646133381864" (x+3)2(x-2)=0(x+3)=0;(x-2)=0x=-3;x=2

Thus, the x-intercepts are:x=-3,2

02

Part (b) Step 1. Substitute x with x+3

We have,

G(x+3)=(x+3+3)2(x+3-2)G(x+3)=(x+6)2(x+1)

03

Part (b) Step 2. Find the x-intercept of G(x+3)

(x+6)2(x+1)=0(x+6)=0;(x+1)=0x=-6;x=-1

So, the x-intercepts are-6,-1

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