Question

If we express $2x^2 + 6x + 11$ in the form $a(x - h)^2 + k$, then what is $h$? (ignore the $)

Answer 1

-3/2

Explanation:

We complete the square. First, we factor 2 out of the terms $2x^2 + 6x$ to get $2(x^2 + 3x)$. We can square $x + 3/2$ to get $x^2 + 3x + 9/4$, so $h = \boxed{-3/2}$.

Answer 2

2x^2+6x+11 = 2(x+3/2)^2 + 11 - 9/2,

so h = 11 - 9/2 = 13/2