Question

Y = 2(x+2)^2 - 18Find the x intercepts

Answer 1

Answer

x=-5

and

x=1

Explanation

The equation y = 2(x+2)^2 - 18 corresponds to a translation 2 units left and 18 units down, and a and a shrinkage about the x-axis with factor 2.

Making these transformations to y=x^2, we have:

$y=2(x+2)^2-18$$y=2(x{}^2+4x+4)-18$$y=2x^2+8x+8-18$$y=2x^2+8x-10$

Factoring:

$y=2(x^2+4x-5)$$y=2(x+5)(x-1)$

The x-intercept are found when y=0, that is:

$\begin{gathered} x+5=0 \\ x=-5 \end{gathered}$

and

$\begin{gathered} x-1=0 \\ x=1 \end{gathered}$