# What is the axis of symmetry and vertex for the graph y = 1/2x^2 + 6x?

Mar 29, 2017

minimum vertex $- 18$ with axis symetry at $x = - 6$

#### Explanation:

we can solve it by using completing a square.

$y = \frac{1}{2} {x}^{2} + 6 x = \frac{1}{2} \left({x}^{2} + 12 x\right)$

$y = \frac{1}{2} {\left(x + 6\right)}^{2} - \frac{1}{2} {\left(6\right)}^{2}$

$y = \frac{1}{2} {\left(x + 6\right)}^{2} - 18$

since a coefficient of ${\left(x + 6\right)}^{2}$has +ve value, it has a minimum vertex $- 18$ with axis symetry at $x = - 6$