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

May 31, 2015

I change the notation for easy understanding.

y = 2x^2 - 28x + 116

x of vertex: $x = \left(- \frac{b}{2} a\right) = \frac{28}{4} = 7$

y of vertex: $f \left(7\right) = 2. \left(49\right) - 28 \left(7\right) + 116 = 98 - 196 + 116 = 18$

Vertex form $f \left(x\right) = 2 {\left(x - 7\right)}^{2} + 18$

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

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