Exploring Vertex Form

Exploration
A quadratic function can be written in Vertex Form [math]f\left(x\right)=a\left(x-h\right)^2+k[/math], where the variables [math]a,[/math] [math]h,[/math] and [math]k[/math] control different transformations. One at a time, move each slider and notice how it is changing the quadratic parent function [math]f\left(x\right)=x^2[/math].
How does changing the [math]a[/math] value affect the graph?
How does changing the [math]h[/math] value affect the graph?
How does changing the [math]k[/math] value affect the graph?
One at a time, turn on each equation and use the sliders to match the black quadratic parent function with the new transformed function.
Input different values for a, h, and k until the red parabola models a trajectory that will launch the Angry Bird in the catapult into the green pig.
Record the equation you created to model the Angry Bird situation here.
Check and un-check the boxes to see how the parabola is affected when it is reflected over the x-axis and y-axis.
What do you notice when the parabola is reflected over the x-axis? y-axis?
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– madeline.gage

Information: Exploring Vertex Form