Question

How do you find the axis of symmetry, graph and find the maximum or minimum value of the function `y =3(x-3)^2 - 4`?

Answer 1

Minimum value is `-4`.
Axis of symmetry is `x=3`.
Use the vertex and the `a-value` to help outline what the parabola will look like.

Explanation:

So the function you gave us is in vertex form. This makes finding max/min value, axis of symmetry, and graphing exponentially easier (well at least to me).

The maximum/minimum value is simply the `k` value in vertex form. In this case, the minimum value is `-4`. It is minimum because the parabola opens up.

The axis of symmetry, is just the `x-value` of the vertex. It is also an equation. In this case, the vertex is `(3, -4)`. Therefore, the axis of symmetry is `x=3`.

Lastly, graphing the parabola is made easier in vertex form, because you're given the vertex (it's right there), and you know the `a-value`
=> you know how much the parabola is going to stretch.

An easy way to graph a parabola is to use the "input-output" method. Input is the x-axis, while output is the y-axis. You are always looking for the y-axis (with this method), and the input is always 1 number higher or lower than the vertex. You continue to increase the x-value by 1.

As a result, the parabola will look like this:

Hope this helps :)

P.S. This graphing program is called Desmos. It's a very good program that I recommend to others that struggle visualizing what the parabola looks like.