Find a function f whose graph is a parabola with the given vertex and that passes through the given point. vertex (−1, 5); point (−3, −3) f(x) =

Answer 1

A quadratic function (parabolic graph) can be expressed as f(x) = a(x - h)² + k, where (h,k) is the vertex.

So, for the given function, we have f(x) = a(x + 1)² + 5.

Since (-3,-3) is on the graph, f(-3) = -3.

So, -3 = a(-2)² + 5.

Therefore, a = -2.

f(x) = -2(x + 1)² + 5