Parabola intuition 1

The  exercise appears under the Algebra I Math Mission. This exercise explores horizontal and vertical translations, as well as simple vertical dilations.

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


 * 1) Adjust the values to make the 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.Parint1-1.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.