# How do you find the axis of symmetry, and the maximum or minimum value of the function y = −3x^2 − 12x + 5?

Jan 23, 2016

The axis of symmetry is $x = - 2$.
The vertex is $\left(- 2 , 17\right)$.

#### Explanation:

$y = - 3 {x}^{2} - 12 x + 5$ is in standard form, $a {x}^{2} + b x + c$, where a=-3, b=-12, and c=5".

The axis of symmetry is an imaginary vertical line that separates the parabola into two equal halves. The formula for the axis of symmetry is $x = \frac{- b}{2 a}$.

$x = \frac{- \left(- 12\right)}{2 \cdot - 3} =$

$x = \frac{12}{- 6} =$

$x = - 2$

This is also the $x$ value of the vertex, which is the maximum point of this parabola. We can know that the vertex is the maximum point because when $a < 0$, the parabola opens downward.

To find the $y$ value for the vertex, substitute $- 2$ for $x$ in the equation and solve for $y$.

$y = - 3 {x}^{2} - 12 x + 5$

$y = - 3 {\left(- 2\right)}^{2} - 12 \left(- 2\right) + 5 =$

$y = - 3 \left(4\right) + 24 + 5 =$

$y = - 12 + 24 + 5 =$

$y = 17$

The vertex is $\left(- 2 , 17\right)$.

graph{y=-3x^2-12x+5 [-9.64, 10.36, 7.694, 17.69]}