Answer :
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:
[tex]y=2(x+2)^2-18[/tex][tex]y=2(x{}^2+4x+4)-18[/tex][tex]y=2x^2+8x+8-18[/tex][tex]y=2x^2+8x-10[/tex]Factoring:
[tex]y=2(x^2+4x-5)[/tex][tex]y=2(x+5)(x-1)[/tex]The x-intercept are found when y=0, that is:
[tex]\begin{gathered} x+5=0 \\ x=-5 \end{gathered}[/tex]and
[tex]\begin{gathered} x-1=0 \\ x=1 \end{gathered}[/tex]