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Chapter 10: Q. 40 (page 644)

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

x2=-4y

Short Answer

Expert verified

The vertex is 0,0focus is 0,-1and the directrix is y=1.

The graph of the equation x2=-4y.

Step by step solution

01

Step 1. Given information .

Consider the given equationx2=-4y.

02

Step 2. Analyze the equation .

The standard form of parabola is x2=-4ay

Compare the equation with standard form.

x2=-4ayx2=-4y-4a=-4a=1

Further simplify.

Since the value of a=1the vertex is 0,0,the focus is 0,-a=0,-1and the directrix isy=a,y=1.

03

Step 3. Plot the graph .

The graph of the equation x2=-4yby using graphic utility just shown below.

Here V is the vertex ,F is focus and liney=1represents the directrix of the parabola .

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and equations of the parabola areA)y2=4xC)y2=-4xE)(y-1)2=4(x-1)G)(y-1)2=-4(x-1)B)x2=4yD)x2=-4yF)(x+1)2=4(y+1)H)(x+1)2=4(y+1)
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