In this section, a graphing calculator is used to solve quadratic functions.

Follow the steps below to find the x-intercepts of a quadratic function using a graphing calculator.

Example:  Solve x2 − 5x + 3 = 0

Step 1: Enter quadratic equation into calculator for [Y1].


Step 2: Enter y=0 for [Y2].


Step 3: Using left arrow [⇐], move cursor to line descriptor on the left of [Y2] and press [ENTER] to bold this line.


Step 4:[GRAPH] (Notice, y=0 is a bold line on the y-axis.)


Step 5: Choose [2nd][TRACE] to get the CALCULATE menu.


Step 6:Since the x-intercept (or zero or root) is where the graph intersects the x-axis, choose 5: intersect [ENTER].


Step 7: Move the cursor or blinking light to one of the x-intercepts.


Step 8: When the question "First Curve?" appears on the screen make sure your cursor is on either the parabola or the x-axis and press [ENTER]. The question "Second curve?" should appear. Check to be sure your cursor is on the other curve. Press [ENTER]. The question "Guess?" should appear. Move your cursor close to the intersection you are trying to find and press [ENTER]. One of the x-intercepts is (0.70, 0).


Step 9: Repeat steps 5 to 8 to get the second x-intercept. The solution set is {0.70, 4.30}.


The following problem is an example of finding a solution when it is difficult to see where the graph of the quadratic equation touches the x-axis.

Example: Solve 0 = -2x2 + 3x - 1

Step 1: Enter quadratic equation into calculator for [Y1].


Step 2: Enter 0 for [Y2]


Step 3: Using left arrow [⇐], move cursor to line descriptor on the left of [Y2] and press [ENTER] to bold this line.


Step 4: [GRAPH] (Notice, y=0 is a bold line on the y-axis.)

It appears that there could be one or two x-intercepts.


Step 5: To get a closer look, you can zoom in by choosing [ZOOM].


Step 6:< Then choose 2:Zoom In


Step 7: Move blinking light to the area you want to zoom in to. Press [ENTER] as many times as needed to get a clear window.


Step 8: Choose [2nd][TRACE] to get the CALCULATE menu.


Step 9: Next choose 5: intersect [ENTER].


Step 10: Move the cursor or blinking light to one of the x-intercepts.


Step 11: When the question "First Curve?" appears on the screen make sure your cursor is on either the parabola or the x-axis and press [ENTER]. The question "Second curve?" should appear. Check to be sure your cursor is on the other curve. Press [ENTER]. The question "Guess?" should appear. Move your cursor close to the intersection you are trying to find and press [ENTER].


Step 12: Repeat steps 8 to 11 to get second x-intercept.
The solution set is {0.5, 1}


Solve the following quadratic equations using a graphing calculator. Round to nearest hundredth.

  1. 4x2 + 3x = 12 Interactive popup. Assistance may be required. Check Your Answer {-2.15, 1.40}
    Close Pop Up
  2. 0 = -2x2 − 7x − 6 Interactive popup. Assistance may be required. Check Your Answer {-1.5, -2}
    Close Pop Up
  3. x2 = 14x − 49 Interactive popup. Assistance may be required. Check Your Answer {7}
    Close Pop Up

In your notes, describe how to use the table method in conjunction with the graphing method to solve a quadratic equation.