Transformations of Quadratic Functions

We want to draw the graph of the given function, which has the form $y=x^2+k,$ where $k$ is either a positive or a negative number. $\begin{gathered} y=x^2-9 \end{gathered}$ To do so, we will first draw the graph of its parent function, $y=x^2.$ Recall that the graph of $y=x^2$ is a parabola opening upwards, with vertex $(0,0),$ whose axis of symmetry is the vertical line $x=0,$ and passes through the points $(3,9)$ and $(\text{-} 3,9).$

Our function is a vertical translation of the parent function by $9$ units in the negative direction. Thus, we will translate the above graph $9$ units downwards.