Transformations of a Parabola

Use the slider to investigate how changing the value of a affects the graph of the parabola. The parent parabola is shown in black.
How does changing the value of a in [math]y=ax^2[/math]affect the graph of the parabola? Select all that apply.
Use the slider to investigate how changing the value of h affects the graph of the parabola. The parent parabola is shown in black.
How does changing the value of h in [math]y=\left(x-h\right)^2[/math]affect the graph of the parabola?
Use the slider to investigate how changing the value of k affects the graph of the parabola. The parent parabola is shown in black.
How does changing the value of k affect the graph of [math]y=x^2+k[/math]? Select all that apply.
Putting It All Together
Use the sliders to investigate how changing the values in the vertex form of a parabola changes the graph. The parent parabola is shown in black.
Where is the vertex of [math]y=-2\left(x-4\right)^2+2[/math]? Place your answer in parentheses.
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Information: Transformations of a Parabola