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 directrix is $y=-1$.

The graph for the equation is shown below.

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 $a=1$the vertex of parabola is $\left(0,0\right)$,focus is role="math" localid="1646807678978" $\left(0,a\right)=\left(0,1\right)$.

The directrix is $y=-a$that means$y=-1$

Step 3. Plot the graph.

The graph of the parabola equation, $x^2=4y$using graphic utility is shown below.

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