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Chapter 6: Q. 314 (page 627)

For the function, f(x)=x2+11x+20:

a. find x, when f(x)=-8.

b. Use this information to find two points that lie on the graph of the function.

Short Answer

Expert verified

a. The value of xis -4or -7when f(x)=-8.

b.(-4,-8)and(-7,-8)lie on the graph of the function.

Step by step solution

01

Part a. Find x when f(x)=-8.

Substitute f(x)=-8in the given equation,

f(x)=x2+11x+20-8=x2+11x+20x2+11x+28=0x2+4x+7x+28=0x(x+4)+7(x+4)=0(x+4)(x+7)=0

Using Zero Product Property,

x+4=0or

x+7=0.

When x+4=0,

x=-4.

When x+7=0,

x=-7.

Checking each value separately,

when x=-4,

f(x)=x2+11x+20f(-4)=-42+11(-4)+20f(-4)=16-44+20f(-4)=-8

This is true.

When x=-7,

f(x)=x2+11x+20f(-7)=(-7)2+11(-7)+20f(-7)=49-77+20f(-7)=-8

This is true too.

02

Part b. Find points that lie on the graph of the function

Since f(-4)=-8and f(-7)=-8, the points (-4,-8)and (-7,-8)lie on the graph of the given function.

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