Our factored equation is going to be something like:
y = a (x-4)(x+8)
So now we have to solve for a. Just plug in the point (2,10)
y = a (x-4)(x+8)
10 = a(2-4)(2+8)
10 = a(-2)(10)
10 = -20a
10/-20 = a
-1/2 = a
So the equation is y=-1/2(x-4)(x+8)
a) factored form: y=-1/2(x-4)(x+8)
b) standard form: -1/2*x^2-2x+16
c) vertex form: y=-1/2*(x+2)^2+18
If you graph all 3, it should be the same line
y=-1/2*x^2+-2*x+16
y=-1/2*(x^2+4*x+-32) ( Factor out )
y=-1/2*(x^2+4*x+(2)^2+-1*(2)^2+-32) ( Complete the square )
y=-1/2*((x+2)^2+-1*(2)^2+-32) ( Use the binomial formula )
y=-1/2*((x+2)^2+-36) ( simplify )
y=-1/2*(x+2)^2+18