Bigger picture

A certain point of view

Click on the Animate button in the applet below or move the slider.

What is happening in the animation as the value of $u$ increases from $0$ to $1$?

Which characteristics of the parabola are being preserved and which are being changed?

How can we describe the transformation that is happening to the parabola?

What can we say about the transformed parabola?

Can we use the transformed parabola to find the equation of the original parabola, $y=f(x)$?