Parabolas and quadratic functions II

Focus and Directrix

I. The equation of a parabola with focus $(p,q)$ and directrix $y=l$ is:

_____________________________________

II. The focus and directrix of the parabola $y=ax^2+bx+c$ are:

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Roots

I. If a quadratic $f(x)$ has roots $r_1$ and $r_2$, then the formula for $f(x)$ is ____________________________________

II. Given a quadratic function $f(x)=ax^2+bx+c$, the formula for the roots is: ____________________________________

Applying transformations to $y=x^2$

I. If we translate the graph of $y=x^2$ by $(h,k)$, then the resulting parabola has equation $y =$_________________________

II. If we reflect the graph of $y=x^2$ across the $x$-axis, then the resulting parabola has equation $ y=$_________________________

III. If we dilate the graph of $y=x^2$ by a factor of $r$ centered at the origin $(0,0)$, then the resulting parabola has equation $y =$_________________________