Answer:
[tex]y = -\frac{1}{2}(x^2-2x-8)[/tex]
Simplified it is [tex]y=-\frac{1}{2}x^2+x+4[/tex]
Step-by-step explanation:
The x-intercepts of a parabola form the factors of the equation. Since the x -intercepts are (-2,0) and (4,0) then the factors are (x+2) and (x-4). Factors are pieces which multiply to make the equation.
[tex]y=(x+2)(x-4)\\y=x^2+2x-4x-8\\y=x^2-2x-8[/tex]
This is the standard form of the parabola [tex]ax^2+bx+c[/tex]. Since the y-intercept of the parabola is (0,4) then a number must also be multiplied to it
[tex]y=a(x^2-2x-8)[/tex]
We find a by plugging in x=0 and y=4.
[tex]4=a(0^2-2(0)-8)\\4=a(0-0-8)\\4=a(-8)\\\frac{4}{-8} = a\\\frac{-1}{2} = a[/tex]
So the equation is [tex]y = -\frac{1}{2}(x^2-2x-8)[/tex].
When simplified it is [tex]y=-\frac{1}{2}x^2+x+4[/tex]
