Answer:
[tex]y=2(x+1)^2-8[/tex]
Step-by-step explanation:
To write the quadratic equation, begin by writing it in vertex form
[tex]y = a(x-h)^2+k[/tex]
Where (h,k) is the vertex of the parabola.
Here the vertex is (-1,-8). Substitute and write:
[tex]y=a(x--1)^2+-8\\y=a(x+1)^2-8[/tex]
To find a, substitute one point (x,y) from the parabola into the equation and solve for a. Plug in (1,0) a x-intercept of the parabola.
[tex]0=a((1)+1)^2-8\\0=a(2)^2-8\\0=4a-8\\8=4a\\2=a[/tex]
The vertex form of the equation is [tex]y=2(x+1)^2-8[/tex].
