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Chapter 10: Q. 41 (page 644)

Find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility.

y-22=8x+1

Short Answer

Expert verified

The vertex is -1,2,focus is 1,2and directrix is x=-3.

The graph of the equation shown below .

Step by step solution

01

Step 1. Given information .

Consider the given equationy-22=8x+1.

02

Step 2.  Analyze the equation .

The standard form of parabola is y-k2=4ax-h

Compare the given equation with standard form.

y-k2=4ax-hy-22=8x+1

role="math" localid="1646822176449" 4a=8a=2h=-1,k=2

Since the value of a=1the vertex is h,k=-1,2and focus is role="math" localid="1646822293613" h+a,k=1,2and the directrix isx=h-a=-1-2=-3

03

Step 3. Plot the graph.

BY using graphic utility the graph of the given equation y-22=8x+1shown below .

Here V is the vertex ,F is the focus and line x=-3represents the directrix of the parabola .

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