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#?

1 Answer
Mar 29, 2017

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.


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:

Desmos Graphing Calculator

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.