# How do you find the axis of symmetry, graph and find the maximum or minimum value of the function y= 3(x+2)^2-1?

Jul 17, 2018

Minimum (-2, -1); " axis of symmetry: " x = -2

#### Explanation:

Given: $y = 3 {\left(x + 2\right)}^{2} - 1$

The given function is a quadratic equation that is the graph of a parabola.

When the equation is in vertex form: $y = a {\left(x - h\right)}^{2} + k$,

the $\text{vertex": (h, k); " axis of symmetry: } x = h$

The parabola has a minimum when $a > 0$ and a maximum when $a < 0$

the $\text{vertex": (-2, -1); " axis of symmetry: } x = - 2$

the vertex is a minimum since $a = 3 > 0$

To graph just find additional points using point-plotting. Since $x$ is the independent variable, you can select any value of $x$ and calculate the corresponding value of $y$:

$\underline{\text{ "x" "|" "y" }}$
$- 4 \text{ "|" "11" }$
$- 3 \text{ "|" "2" }$
$- 1 \text{ "|" "2" }$
$\text{ "0" "|" "11" }$ This is the $y$-intercept

Graph of $3 {\left(x + 2\right)}^{2} - 1$:
graph{3(x+2)^2 - 1 [-5, 3, -5, 12]}