Question

How do you write `x= 2y^2 - 28y + 116` into vertex form?

Answer 1

I change the notation for easy understanding.

y = 2x^2 - 28x + 116

x of vertex: `x = (-b/2a) = 28/4 = 7`

y of vertex: `f(7) = 2.(49) - 28(7) + 116 = 98 - 196 + 116 = 18`

Vertex form `f(x) = 2(x - 7)^2 + 18`

Check by developing: f(x) = 2(x^2 - 14x + 49) + 18 =

= 2x^2 - 28x + 116. OK