Question

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`?

Answer 1

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

Explanation:

Given: `y = 3(x+2)^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(x - h)^2 + k`,

the `"vertex": (h, k); " axis of symmetry: "x = h`

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

the `"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`:

`ul(" "x" "|" "y" ")`
`-4" "|" "11" "`
`-3" "|" "2" "`
`-1" "|" "2" "`
`" "0" "|" "11" "` This is the `y`-intercept

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