Shift and scale parabolas

The  exercise appears under the Algebra II Math Mission. This exercise practices finding the equation of a parabola by shifting and scaling the basic parabola $$y=x^2$$.

Types of Problems
There is one type of problem in this exercise:


 * 1) Adjust the values to match the other parabola: This problem provides two parabolas and a manipulative to adjust values on a quadratic function. The student is asked to adjust the values correctly to move one parabola on top of the other. Shift and scale parabolas.PNG

Strategies
Knowledge of functional transformations (specifically translations and dilations) could improve efficiency on this exercise.
 * 1) With the $$x$$, subtracting is translation right, and adding is translation left.
 * 2) With the $$y$$, subtracting is translation up, and adding is translation down.
 * 3) Outside the $$x$$, subtracting is translation down, and adding is translating up.
 * 4) Increasing the value of the multiplying coefficient stretches the graph vertically, making it "skinnier".
 * 5) Negative multiplication coefficients reflect a graph over the horizontal axis, making it open downward.

Real-life Applications

 * 1) Parabolas are used to model many physical properties, such as projectile motion.
 * 2) Functional transformations assist understanding functions by requiring less memorization and more understanding of how some functions are inter-related.