# How do you find the axis of symmetry, and the maximum or minimum value of the function f(x) = -3x^2 - 6x - 2?

Mar 22, 2018

Axis of symmetry: $x = - 1$

Vertex: $\left(- 1 , 1\right)$

#### Explanation:

$f \left(x\right) = - 3 {x}^{2} - 6 x - 2$ is a quadratic equation in standard form:

$a {x}^{2} + b x + c$,

where:

$a = - 3$, $b = - 6$, $c = - 2$

Axis of symmetry: vertical line that divides a parabola into two equal halves

The formula for finding the axis of symmetry for a quadratic equation in standard form is:

$x = \frac{- b}{2 a}$

$x = \frac{- \left(- 6\right)}{2 \cdot - 3}$

Simplify.

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

$x = - 1$

The axis of symmetry is $x = - 1$.

Vertex: minimum or maximum point of a parabola

Since $a < 0$, the vertex is the maximum point and the parabola will open downward.

The $x$-value of the vertex is the axis of symmetry.

To find the $y$-value, substitute $- 1$ for $x$, and substitute $f \left(x\right)$ for $y$.

$y = - 3 {\left(- 1\right)}^{2} - 6 \left(- 1\right) - 2$

Simplify.

$y = - 3 + 6 - 2$

$y = 1$

The vertex is $\left(- 1 , 1\right)$.

graph{y=-3x^2-6x-2 [-10, 10, -5, 5]}