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Chapter 10: Q. 53 (page 644)

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

x2-4x=y+4

Short Answer

Expert verified

The vertex is 2,-8, focus is 2,-314and the directrix is y=-334.

The graph of the equation shown below .

Step by step solution

01

Step 1.  Given information .

Consider the given equationx2-4x=y+4.

02

Step 2.  Analyze the equation .

The standard form of the parabola is x-h2=4ay-k.

Compare the given equation with standard form .

role="math" localid="1647088607109" x-h2=4ay-kx-22=y+8a=14h=2,k=-8

Further simplify .

Since the value ofa=14the vertex ish,k=2,-8and focush,k+a=2,-314and the directrix isy=-334.

03

Step 3.  Plot the graph .

The graph of the equation x2-4x=y+4using graphing utility is shown below .

Here V is the vertex , F is focus and the line y=-334represents the directrix of the parabola .

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