This section explores the use of graphs to solve quadratic equations.

Exploration:

Open the applet to explore the solutions or x-intercepts given a graph.

Solving Quadratic Equations Applet

1. Click on the button “click here to start,” which will open the applet in a new window.
2. Enter the a, b, and c and value of the equations listed below by using the scroll bar.

Recall: 0 = ax² + bx + c

3. Identify the solutions visually while comparing to the answers listed in the upper left hand corner of the coordinate plane.

Solve the following quadratic equations using the applet above.

1. 3x² - 10x + 8 = 0
   Interactive popup. Assistance may be required. Check Your Answer x = 2 or x = 1 one-third 1 3
   
2. 14u² = -13u - 3 (zoom out)
   Interactive popup. Assistance may be required. Check your answer x = - one-half 1 2 or x = -.43
   
3. -2x = x² + 3
   Interactive popup. Assistance may be required. Check your answer No real solution
   
4. 9(x + two-thirds 2 3 )² = 0
   Interactive popup. Assistance may be required. Check your answer x = - two-thirds 2 3