# Investigating Quadratic Functions in Vertex Form

- Author:
- Jeremy Cue

- Topic:
- Functions, Quadratic Functions

Move the sliders one at a time to explore how the values of

*a*,*h*, and*k*affect the graph of the quadratic parent function.How does the value of *a* affect the graph of the quadratic parent function?

How does the value of *h* affect the graph of the quadratic parent function?

How does the value of *k* affect the graph of the quadratic parent function?

## Modeling the Path of a Football

The quarterback throws the football to a wide receiver for a touchdown! Click and drag the football from the quarterback's hand to the wide receiver to show the parabolic path of the football. After you've created the path, use the sliders to find a quadratic function that models the path of the football.
In this problem,

*x*represents the horizontal distance of the football (in yards), and*y*represents the height of the football (in yards).What is the equation of the quadratic function that models the path of the football?

What is the maximum height of the football? Is this value related to *a*, *h*, or *k*?