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Chapter 4: Q. 108 (page 195)

h(x)=(x+2)(x-4)3

(a) Identify the x-intercepts of the graph of h.

(b) What are the x-intercepts of the graph of y=h(x-2)?

Short Answer

Expert verified

(a) x-intercepts ofh(x)are-2,4

(b) x-intercepts ofh(x-2)are0,6

Step by step solution

01

Part (a) Step 1.  Solve for x

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

(x+2)(x-4)3=0x+2=0;x-4=0x=-2;x=4

So, the x-intercepts are-2,4

02

Part (b) Step 1. Substitute x with x-2

h(x-2)=(x-2+2)(x-2-4)3h(x-2)=x(x-6)3We have,

03

Part (b) Step 2. Find the x-intercepts of h(x-2)

x(x-6)3=0x=0;x-6=0x=0;x=6

So, the x-intercepts ofh(x-2)is0,6

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