How do I write the standard form?

Question

Given the vertex(1,-5) and the point (-1,11) write the standard form of the quadratic function whose graph is a parabola with those points.

Answer 1

Plug the vertex into the vertex form of a parabola

y=a(x-h)²+k where (h,k) is the vertex

y=a(x-1)²-5

plug the point (-1,11) into the above to get the a

11=a(-1-1)²-5

11=a(-2)²-5

11=a(4)-5

Add 5 to both sides

16=4a

Divide by 4

a=4

Plug a back into vertex form

y=4(x-1)²-5

y=4(x-1)(x-1)-5

Foil

y=4(x²-x-x+1)-5

y=4(x²-2x+1)-5

Distribute

y=4x²-8x+4-5

Standard form is

y=4x²-8x-1