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Chapter 10: Q. 48 (page 644)

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

x2+6x-4y+1=0

Short Answer

Expert verified

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

The graph of the given equation shown below.

Step by step solution

01

Step 1. Given information.

Consider the given equation x2+6x-4y+1=0.

02

Step 2. Analyze the equation .

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

Compare the given equation with standard form.

x-h2=4ay+kx+32=4y+24a=4a=1h=-3,k=-2

Further simplify.

Since the value ofa=1then the focus ish,k+a=-3,-1,vertex ish,k=-3,-2and the directrix isy=k-a=-3

03

Step 3. Plot the graph .

Using the graphing utility the graph of the given equation x2+6x-4y+1=0just shown below .

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

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