Answer:
[tex]y=2x^2+8x-12[/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 (-2,-20). Substitute and write:
[tex]y=a(x--2)^2+-20\\y=a(x+2)^2-20[/tex]
To find a, substitute one point (x,y) from the parabola into the equation and solve for a. Plug in (0,-12) the y-intercept of the parabola.
[tex]-12=a((0)+2)^2-20\\-12=a(2)^2-20\\-12=4a-20\\8=4a\\2=a[/tex]
The vertex form of the equation is [tex]y=2(x+2)^2-20[/tex].
You can convert this into standard form by using the distributive property.
[tex]y=2(x+2)^2-20\\y=2(x^2+4x+4)-20\\y=2x^2+8x+8-20\\y=2x^2+8x-12[/tex]
