Question

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

Answer 1

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

Explanation:

we can solve it by using completing a square.

`y = 1/2 x^2 + 6 x = 1/2(x^2 +12 x)`

`y = 1/2(x +6 )^2 - 1/2 (6)^2`

`y = 1/2(x +6 )^2 - 18`

since a coefficient of `(x + 6)^2`has +ve value, it has a minimum vertex `-18` with axis symetry at `x = -6`