Question

Suppose f(x) = 2x + 8 and h(x) = 2x-8. Which statements correctly describe t(x) = f(x)×h(x)? Select all that apply. •The graph of t(x) intersects the x-axis at (-8,0) and (8,0)•The y-intercept of the graph of t(x) is (0, -16)•t(x) = 4x^2 - 32x +64 •The zeros of t(x) are x= -1/4 and x=1/4•The zeros of t(x) are x= -4 and x=4 •The y-intercept of the graph of t(x) is (0, -64)•The function t(x) is the product of conjugatest(x)=4x² – 32x-64 t(x) = 42² – 64

Answer 1

Given data:

The first function given is f(x)=2x + 8.

The second function given is h(x) = 2x-8.

The expression for t(x) is,

$\begin{gathered} t(x)=f(x)\times h(x) \\ =(2x+8)\times(2x-8) \\ =4x^2-64 \end{gathered}$

The x-intercepts are the points where y coordinate is zero.

$\begin{gathered} 0=4x^2-64 \\ 64=4x^2 \\ x^2=16 \\ x=4,-4 \end{gathered}$

The y-intercepts are the points where x coordinate is zero.

$\begin{gathered} y=4(0)^2-64 \\ =-64 \end{gathered}$

Thus, the zeroes of t(x) are 4, -4, the y-intercept of the graph is (0, -64) and t(x)=4x^2 -64.