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Chapter 9: TRY IT : : 9.90 (page 930)

Find the intercepts of the parabola whose function is f(x)=x2鈭�4x鈭�12.

Short Answer

Expert verified
  • The y-intercept is the point (0, 鈭�12) .
  • The x-intercepts are the points (6, 0) and (鈭�2, 0) .

Step by step solution

01

Step 1. Given information

Consider the function

f(x)=x2鈭�4x鈭�12.

02

Step 2. To find the y-intercept, let x = 0 and solve for f (x) .

f(x)=x2鈭�4x鈭�12f(0)=(0)2鈭�4(0)鈭�12f(0)=鈭�12

When x = 0 , then f (0) = 鈭�12 .

The y-intercept is the point (0, 鈭�12) .

03

Step 3. To find the x-intercept, let f (x) = 0 and solve for x .

f(x)=x2鈭�4x鈭�120=x2鈭�4x鈭�12

Solve by factoring.

0=(x-6)(x+2)0=x-6;0=x+26=x;-2=x

When f (x) = 0 , then x = 6 or x = 鈭�2 .

The x-intercepts are the points (6, 0) and (鈭�2, 0) .

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