Let’s say we want to graph the function f(x) = (-1/3)x2 + 2x – 3.
1.) Press the Y= button and enter in the right side of the equation. Don’t forget to square the first x!
2.) Press GRAPH to view your parabola.
3.) In order to graph parabolas well, we need to find the vertex. I cover this in more detail in my video and TI-84 How To article entitled Graphing Calculator: How To Find the Vertex of a Parabola.
a.) Press 2nd, Calc.
b.) Select either maximum or minimum. In this case, we will select maximum, because the vertex occurs on the highest point on the parabola.
c.) Choose your left down, right down, and then “guess” where your vertex is by moving the cursor as close as you can to it. Then press enter.
The vertex of this function is (3, 0).
Now we need to find the coordinates of some other points on the parabola, so that we can draw an accurate looking graph.
We could do this by hand by substituting values of x into the equation and finding their respective y-values.
However, we can save a lot of work by calculating a table of values on the TI-84. How to do this is in my explanation below.
4.) Simply press 2nd, GRAPH, and the calculator will show you the table of values for this function.
5.) Now we want to select some points from this table to graph. I recommend selecting 3 points to the left of the vertex, and 3 points to the right of the vertex. In this example, I shall pick (2, -1/3), (1, -4/3), (4, -1/3), (5, -4/3), (6, -3), (0, -3).
6.) Now, all we need to do is graph these points on graph paper. Note that some of these points have fractional Y values. To plot these points, you need to estimate where the point with a y-value of one third and four thirds would be.
7.) Once you have plotted the points, connect the dots with the curve.