Question

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

39. vertex (1, 7), directrix y = 3.

Short answer

The equation of the parabola is $y=2{\left(x-1\right)}^2+7$.

The graph is:

Step-by-step solution

Step 1. Given

Vertex (1, 7), directrix $y=3$.

Step 2. To determine

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

Step 3. Calculation

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

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

Vertex = $(h,k)=(1,7)$

$\begin{array}{c}2a=\text{Distance\hspace{0.17em}\hspace{0.17em}between\hspace{0.17em}\hspace{0.17em}vertex\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}directrix}\\ =7-3\\ =4\end{array}$

So, $a=2$

So, the equation becomes:

$\begin{array}{c}y=a{\left(x-h\right)}^2+k\\ y=2{\left(x-1\right)}^2+7\end{array}$

Using a graphing calculator, the graph is: