Question

3. *Which of the following equations has x intercepts at 4 and -2? (A) y = 3x^2 - 10x - 8 (B) y = x^2 + 2x - 8 (C) y = 3x^2 – 2x – 8 (D) y = x^2 - 2x - 8

Answer 1

Given data:

The x-intercepts given are 4 and -2.

Substitute 0 for y in the first option.

`\begin{gathered} 0=3x^2-10x-8 \\ 3x^2-12x+2x-8=0 \\ 3x(x-4)+2(x-4)=0 \\ x=4,\text{ -}(2)/(3) \end{gathered}`

Substitute 0 for y in the second option.

`\begin{gathered} 0=x^2+2x-8 \\ x^2+2x-8=0 \\ x^2+4x-2x-8=0 \\ x(x+4)-2(x+4)=0 \\ (x-2)(x+4)=0 \\ x=2,\text{ -4} \end{gathered}`

Substitute 0 for y in the third option.

`\begin{gathered} 0=3x^2-2x-8 \\ 3x^2-2x-8=0 \\ 3x^2-6x+4x-8=0 \\ 3x(x-2)+4(x-2)=0 \\ (x-2)(3x+4)=0 \\ x=2,\text{ -}(4)/(3) \end{gathered}`

Substitute 0 for y inlast option.

`\begin{gathered} 0=x^2-2x-8 \\ x^2-4x+2x-8=0 \\ x(x-4)+2(x-4)=0 \\ (x-4)(x+2)=0 \\ x=4,\text{ -2} \end{gathered}`

Thus, option (D) is correct.