Exploring Solutions to Parabolas
Instructions
By the end of this activity, you (the student) should understand have a stronger understanding of what types of solutions a parabola can have.
For this activity, we have a picture of a stained glass window from the Buley Library at Southern Connecticut State University.
At the moment, your a, b, and c values should be equal to zero. Please adjust a, b, and c and record your observations of how the parabola behaves. You can use your mouse to adjust the sliders, and for more precise changes, you can use the arrow keys on your keyboard as well.
What does it mean for a parabola to have 2 real solutions? 1 real solution? Non-real solutions?
Shift the sliders to make a parabola, and when you've made one, write down its equation. Using the quadratic equation, solve for its roots. Are the solutions real or non-real? Is there one or two solutions? How do these solutions relate to the graph of your parabola? After you have found the one of the three types of solutions (2 real, 1 real, Non-real), experiment with the parabola to find equations that yield the other two types of solutions. Type the equations you used and their solutions in the answer box below.