Question

Find the quadratic function that has the indicated vertex and whose graph passes through the given point.
Vertex: (-3,5)
Point; (-6,-1)

Answer 1

Vertex form for a parabola is \[y = a(x-h)^2 + k\]where the vertex is at \((h,k)\), and \(a\) is a scaling constant to make the parabola pass through an arbitrary point.

You know the vertex, so you can fill in the values of \(h,k\) (be careful about the signs!) When you have done that, plug in your known point as the values of \(x,y\) and solve for the value of \(a\).