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(21E) Graphs of Quadratic Functions in the form $f\left(x\right)=a\left(x-h\right)^2+k$

Move the slider to see what happens to the graph of $f\left(x\right)=x^2$ as $x^2$ is multiplied by $a$.

If $a\gt1$, as $a$ increases the graph of $ax^2$ is stretched the -axis and the graph looks

If $0\lt a\lt 1$, as $a$ decreases the graph of $ax^2$ is stretched the -axis and the graph looks

Move the slider to see what happens to the graph of $f\left(x\right)=x^2$ as $x^2$ is multiplied by $a$.

If $a\lt 0$, the graph opens .
If $a\lt -1$, as $a$ decreases the graph of $ax^2$ is stretched the -axis and the graph looks

If $-1\lt a\lt 0$, as $a$ increases the graph of $ax^2$ is stretched the -axis and the graph looks