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Chapter 6: Q. 439 (page 637)

find: (a) the zeros of the function. (b) the x-intercepts of the graph of the function. (c) the y-intercept of the graph of the function.

f(x)=64x2-49

Short Answer

Expert verified

(a) The zeroes of the function are x=-78,78

(b) The x-intercepts of the graph of the function are -78,0,78,0

(c) The y-intercepts of the graph of the function are(0,-49)

Step by step solution

01

Step 1. Given

The function isf(x)=64x2-49

02

Step 2. (a) Find the zeroes of the function

For zeroes of the function, substitute f(x)=0.

f(x)=64x2-490=64x2-49(8x+7)(8x-7)=0

So,

x=78,-78

03

Step 3. (b) Find the x-intercepts of the graph of the function.

Put f(x)=0to find x-intercept.

f(x)is 0at x=78,-78

The x-intercept of the graph of the function are 78,0and -78,0

04

Step 4. (c) Find the y-intercepts of the graph of the function.

Put x=0to find the y-intercept.

f(x)=64x2-49f(0)=64(0)2-49f(0)=-49

The y-intercept of the graph of the function is(0,-49)

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