Question

Find a function whose graph is a parabola with vertex (3, -2) and that passes through the point (4, 3).

I don't understand can someone help please​

Answer 1

`y=5(x-3)^2+2`

Explanation:

`y=a(x-h)^2+k\\y=a(x-3)^2-2\\\\3=a(4-3)^2-2\\3=a(1)^2-2\\3=a-2\\5=a\\\\y=5(x-3)^2+2`

By using the vertex form of a parabola, we were able to plug in the vertex (h,k)=(3,-2) and then eventually our point (x,y)=(4,3) to solve for "a" to get the final function.