How do you find the axis of symmetry, graph and find the maximum or minimum value of the function y=3(x3)24?

1 Answer
Mar 29, 2017

Minimum value is 4.
Axis of symmetry is x=3.
Use the vertex and the avalue 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 xvalue 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 avalue
=> 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 CalculatorDesmos 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.