Quadratic Functions, Math help

Question

What is the formula for the quadratic function given the vertex (12,4) and y-intercept being -12?

Answer 1

Start with the vertex form of a quadratic

y=A(x-h)^2 +k where h and k are the coordinates of the vertex so we have

y=a(x-12)^2 + 4

We are told that the y intercept is at -12 so the coordinates of this point are (0,-12) Remember at the y intercept x=0

Substitute these x and y values and we can solve for a

-12 =a(0-12)^2 + 4

-12= a(144) +4

-16 = 144a

a= -1/9

S0 equation is y = -1/9(x-12)^2 +4

If you plot this on your calculator you will see that the vertex is at 12,4 and y intercept is at -12