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Chapter 10: Q. 47 (page 644)

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

y2-4y+4x+4=0

Short Answer

Expert verified

The vertex is -12,2,focus is -32,2and the directrix is x=12.

The graph of the equation shown below.

Step by step solution

01

Step 1. Given information .

Consider the given equationy2-4y+4x+4=0.

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=-4x+2a=-1h=-12,k=2

Further simplify.

Since the value ofa=-1the value of vertexh,k=-12,2,focus is-32,2and the directrix isx=-12-a=12

03

Step 3. Plot the graph .

By using graphing utility the graph of the given equation y2-4y+4x+4=0just shown below.

Here V is the vertex , F is the focus and the line x=12represents the line of the directrix of parabola .

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Most popular questions from this chapter

In Problem, identify the graph of each equation without completing the squares.

2x2+y2-8x+4y+2=0

To graph y=(x+1)2-4, shift the graph of y=x2to the (left/right) _____unit(s) and then (up/down) _____unit(s).

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True or False

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