Transformations of a Parabola

Parabolas have the form y=ax^2. 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.

The value of a affects the width of the parabola. The value of a affects the direction that the parabola opens. If a is positive. the parabola will open up. If a is negative, the parabola will open down. The value of a has no affect on the graph.

Parabolas can also be written as y=(x+h)^2. 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?

Parabolas can also be written as y=x^2+k. 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.

If k is negative, the graph will move down k units. If k is positive, the graph will move down k units. If k is positive, the graph will move up k units. If k is negative, the graph will move up k units.

Putting It All Together - These transformations can all be combined to construct parabolas that are moved around the Cartesian Plane. The video below demonstrates how to graph a quadratic function (parabola). Note that the video makes an error at the star

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.

Where is the vertex of y=2(x+5)^2 - 3? Place your answer in parentheses.