Question

Write an equation for each parabola described below. Then draw the graph.

vertex (-7, 4), axis of symmetry x = - 7, measure of latus rectum 6, a < 0.

Short answer

The equation of the parabola is $x=-\frac{3}{2}{\left(y-4\right)}^2-7$.

The graph is:

Step-by-step solution

Step 1. Given

Vertex (-7, 4), axis of symmetry $x=-7$, measure of latus rectum 6, a < 0

Step 2. To determine

Write an equation for the parabola. Then draw the graph.

Step 3. Calculation

Since the directrix is parallel to the y-axis, so the standard form of the parabola is:

$x=a{\left(y-k\right)}^2+h$.

Vertex = $(h,k)=(-7,4)$

$\begin{array}{c}4a=\text{Measure\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}Latus\hspace{0.17em}\hspace{0.17em}Rectum}\\ =6\end{array}$

And $a<0$.

So, $a=-\frac{6}{4}=-\frac{3}{2}$.

So, the equation becomes:

$\begin{array}{c}x=a{\left(y-k\right)}^2+h\\ x=-\frac{3}{2}{\left(y-4\right)}^2+\left(-7\right)\\ x=-\frac{3}{2}{\left(y-4\right)}^2-7\end{array}$

Using a graphing calculator, the graph is: