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Chapter 8: Q41. (page 424)

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

Expert verified

The equation of the parabola is y=x-42+3.

The graph is:

Step by step solution

01

Step 1. Given

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

02

Step 2. To determine

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

03

Step 3. Calculation

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

y=ax-h2+k

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

localid="1648619872478" 4a=MeasureofLatusRectum=4

And a>0.

So, a=44=1.

So, the equation becomes:

y=ax−h2+ky=1x−42+3y=x−42+3

Using a graphing calculator, the graph is:

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