EXAMPLE 11

Graph the equation $x^{2}=16y$.

Solution  The graph of $x^{2}=16y$ is a parabola of the form $$x^{2}=4ay$$

where $a=4$. Look at Figure 37(c). The graph will open up, with focus at$( 0,4)$. The vertex is at $( 0,0)$. To graph the parabola, we let $y=a;$ that is, let $y=4$. (Any other positive number will also work.) $$\begin{eqnarray*} x^{2} &=&16y \underset{\underset{\color{#0066A7}{\hbox{\(y=a=4\)}}}{\color{#0066A7}{\displaystyle\uparrow }}}{=} 16( 4) =64 \\[-5.6pt] x &=&-8\qquad\hbox{ or }\qquad x=8 \end{eqnarray*}$$

$x^{2}=16y$

The points$( -8,4)$ and$( 8,4)$ are on the parabola and establish its opening. See Figure 38.

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