Question

Find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility.

$y^2=-16x$

Short answer

The vertex is $\left(0,0\right)$,the focus is $\left(4,0\right)$and directrix is $x=a,x=4$.

The graph of the equation shown below.

Step-by-step solution

Step 1. Given information .

Consider the given equation$y^2=-16x$.

Step 2. Analyze the equation .

The standard form of parabola is $y^2=-4ax$

Compare the equation with standard form

.localid="1646816750877" $$\begin{gathered} y^2=-4ax \\ {y}^2=-16x \\ -4a=-16 \\ a=4 \end{gathered}$$

Further simplify .

Since$a=4$the vertex is$\left(0,0\right)$,the focus is$\left(a,0\right)=\left(4,0\right)$and the directrix islocalid="1646988458852" $x=4$

Step 3. Plot the graph .

The graph of the equation $y^2=-16x$using graphic utility is shown below .

Here V is the vertex , F is the focus and line$x=4$represents the directrix of the parabola .