the graph shows a parabola and its directrix. write the equation of the parabola in vertex form.

Answer:

$y=\frac{1}{8}(x - 0)^2- 3$

Explanation:

Step1: Identify vertex

The vertex of the parabola is at $(h,k)=(0, - 3)$.

Step2: Determine distance from vertex to directrix

The directrix is $y=-6$. The distance $p$ from the vertex $(0,-3)$ to the directrix $y = - 6$ is $|-3-(-6)|=3$. Since the parabola opens up, $p>0$.

Step3: Use vertex - form formula

The vertex - form of a parabola is $y=a(x - h)^2+k$, where $a=\frac{1}{4p}$. Substituting $p = 3$ gives $a=\frac{1}{4\times3}=\frac{1}{8}$, $h = 0$ and $k=-3$ into the formula, we get $y=\frac{1}{8}(x - 0)^2-3$.