The vertext of a quadratic function - Determine an equation

Question

Determine the equation of the quadratic function with vertex (1,5) and passing through the point (-2,32).

Answer 1

You're given the vertex (1,5) and a point (-2,32). You can use the vertex-form of the parabolic equation to solve for this equation. It's a two-step process.

First, you have to solve for a in the formula y=a(x-h)²+k where h and k are the x- and y-coordinates of the vertex (so 1 and 5, respectively). You can plug in the values of h and k as well as x and y into the equation, leaving only 1 remaining variable to solve for: a.

32=a(-2-1)²+5

32=a(-3)²+5

32=9a+5

27=9a

a=3

Second, plug h, k, and a back into the vertex parabola equation and simplify to get the standard form of the quadratic function.

Answer 2

f(x) = a(x - h)² + k, vertex form

f(x) = a(x - 1)² + 5, with given vertex

32 = a(-2 - 2)² + 5, passing through point.

Can you solve for a and answer?