Question

Image: The parabola declines through 4, -1 drops to 5, -3 then increases to 6, -1.

What is the equation for the function in the graph?

Answer 1

The parabola has vertex at (5, −3) (symmetric points (4, −1) and (6, −1) show axis x = 5). Use vertex form y = a(x − 5)^2 − 3.
Plug in (4, −1): −1 = a(4 − 5)^2 − 3 ⇒ −1 = a − 3 ⇒ a = 2.

So y = 2(x − 5)^2 − 3. (Expanded: y = 2x^2 − 20x + 47.)