# How do you find the axis of symmetry, graph and find the maximum or minimum value of the function  y=-3x^2?

Jul 23, 2018

Maximum at $\left(0 , 0\right)$; axis of symmetry at $x = 0$

#### Explanation:

Given: $y = - 3 {x}^{2}$

When the equation is in $y = A {x}^{2} + B x + C = 0$ form:

The vertex is $\left(- \frac{B}{2 A} , f \left(- \frac{B}{2 A}\right)\right)$ and

the axis of symmetry is $x = - \frac{B}{2 A}$

$- \frac{B}{2 A} = - \frac{0}{-} 3 = 0$

$f \left(0\right) = - 3 \left({0}^{2}\right) = 0$

Maximum is at the vertex $\left(0 , 0\right)$, axis of symmetry $x = 0$

To find more points, use point plotting. Since $x$ is the independent variable, select any $x$ and calculate the corresponding $y$:

$\underline{\text{ "x" "|" "y" }}$
$\text{ "-2" } | - 12$
$\text{ "-1" } | - 3$
$\text{ "1" } | - 3$
$\text{ "2" } | - 12$

Graph of $y = - 3 {x}^{2}$:

graph{-3x^2 [-5, 5, -15, 5]}