Matt W. answered • 04/04/19

Cornell Math and Science Tutor with Engineering Background

Let's start by looking at a generic quadratic function in vertex form:

y = a(x-h)^{2}+b

Notice if x = h, then the function becomes y = b. This is either the minimum or maximum of the function with a vertex at (h,b).

if x = 0, then the function becomes y = ah^{2} + b. This is the y intercept!

So putting it together...

If the vertex is (5,4) then this corresponds to (h,b). h = 5 and b = 4.

Plug these numbers back into the original equation:

y = a(x-5)^{2} + 4

Now, substitute the y intercept, y = 2, (when x=0) and solve for a:

2 = a(0-5)^{2} + 4

2 = a(5^{2}) + 4

2 = 25a + 4

a = (-2/25)