# Quadratic Functions (Transformations and Roots)

- Author:
- Jessica Tentinger, Tim Brzezinski

- Topic:
- Functions, Quadratic Functions, Root

Applet contains 3 sliders: "a" slider, "h" slider, and "k" slider.
The equation of any quadratic function (with "a" not = to zero) is ALWAYS a parabola.
Move the sliders around to see the changes in the equation of a the displayed parabola. (The equation will change as you move any slider.)
Questions are contained below the applet.

Questions:
Parameters
1) What effect(s) does the parameter "a" have on the graph (parabola)? Explain in detail.
2) What effect(s) does the parameter "h" have on the graph (parabola)? Explain in detail.
3) What effect(s) does the parameter "k" have on the graph (parabola)? Explain in detail.
4) Write a general equation of a parabola using "a", "h", and "k".
5) Are the coordinates (x, y) of the vertex of the parabola made evident in its equation? If so, how? Explain in detail.
Now look at the roots as you move the sliders.
6) Describe what the parameters have to be in order to have two roots.
7) Describe what the parameters have to be in order to have one root.
8) Describe what the parameters have to be in order to have no roots.
Originally Created by Tim Brzezinski and Modified by Jessica Tentinger