Question

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

vertex (4, 3), axis of symmetry x = 4, measure of latus rectum 4, a > 0.

Short answer

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

The graph is:

Step-by-step solution

Step 1. Given

Vertex (4, 3), axis of symmetry x = 4, measure of latus rectum 4, 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 x-axis, so the standard form of the parabola is:

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

Vertex = $(h,k)=(4,3)$

localid="1648619872478" $\begin{array}{l}4a=\text{MeasureofLatusRectum}\\ =4\end{array}$

And $a>0$.

So, $a=\frac{4}{4}=1$.

So, the equation becomes:

$\begin{array}{l}y=a{\left(x-h\right)}^2+k\\ y=1{\left(x-4\right)}^2+3\\ y={\left(x-4\right)}^2+3\end{array}$

Using a graphing calculator, the graph is: