Question

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

$x^2=-4y$

Short answer

The vertex is $\left(0,0\right)$focus is $\left(0,-1\right)$and the directrix is $y=1$.

The graph of the equation $x^2=-4y$.

Step-by-step solution

Step 1. Given information .

Consider the given equation$x^2=-4y$.

Step 2. Analyze the equation .

The standard form of parabola is $x^2=-4ay$

Compare the equation with standard form.

$$\begin{gathered} x^2=-4ay \\ {x}^2=-4y \\ -4a=-4 \\ a=1 \end{gathered}$$

Further simplify.

Since the value of $a=1$the vertex is $\left(0,0\right)$,the focus is $\left(0,-a\right)=\left(0,-1\right)$and the directrix is$y=a,y=1$.

Step 3. Plot the graph .

The graph of the equation $x^2=-4y$by using graphic utility just shown below.

Here V is the vertex ,F is focus and line$y=1$represents the directrix of the parabola .