Parabola: Quick Anatomy Exploration

Interact with this app for several minutes. As you do, be sure to move the parabola's vertex (V) and focus(F) around. Be sure to interact with the sliders (lower right) as well.

Suppose the equation of a parabola is [math]\left(x-h\right)^2=4p\left(y-k\right)[/math]. [br]Suppose the equation of another parabola is [math]\left(y-k\right)^2=4p\left(x-h\right)[/math]. [br][br]How does messing with [math]h[/math] affect the graph of a parabola?

Moves it down Moves it up Moves it left Moves it right

Suppose the equation of a parabola is [math]\left(x-h\right)^2=4p\left(y-k\right)[/math]. [br]Suppose the equation of another parabola is [math]\left(y-k\right)^2=4p\left(x-h\right)[/math]. [br][br]How does messing with [math]k[/math] affect the graph of a parabola?

Moves it down Moves it right Moves it left Moves it up

A parabola with equation [math]\left(y-k\right)^2=4p\left(x-h\right)[/math] where [math]p>0[/math]

opens downward opens left opens right opens upward

A parabola with equation [math]\left(x-h\right)^2=4p\left(y-k\right)[/math] where [math]p<0[/math]

opens downward opens right opens upward opens left

A parabola with equation [math]\left(y-k\right)^2=4p\left(x-h\right)[/math] where [math]h>0[/math] and [math]k>0[/math]

can open upward can open right can open downward can open left

What exactly does [math]p[/math] tell us? Be specific.

What exactly do [math]h[/math] and [math]k[/math] tell us? Be specific.

Parabola: Quick Anatomy Exploration

Interact with this app for several minutes. As you do, be sure to move the parabola's vertex (V) and focus(F) around. Be sure to interact with the sliders (lower right) as well.

Information: Parabola: Quick Anatomy Exploration