Question

A quadratic function has a vertex at (2,5) and passes through the point (4,9).

What is the correct algorithm for finding an equation for the quadratic function?

Answer 1

Since another way to write an equation for a parabola is a(x-h)^2-k, with h and k as the vertex points, we can plug that in to get a(x-2)^2-5. To find a, we plug 4 in and have 9 as what it equals, getting a(4-2)^2-5=9=4a-5=9 and 4a=14, where a=14/4. Therefore, the equation would be (14/4)(x-2)^2-5