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Chapter 10: Q. 54 (page 644)

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

y2+12y=-x+1

Short Answer

Expert verified

The vertex is 37,-6and the directrix is x=1494.

The graph for the equation shown below .

Step by step solution

01

Step 1.  Given information .

Consider the give equationy2+12y=-x+1.

02

Step 2.  Analyze the equation .

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

Compare the given equation with standard form .

y-k2=4ax-hy+62=-x+37a=-14h=37,k=-6

Further simplify .

Sincea=-14the vertex is37,-6and the directrix isx=1494.

03

Step 3.  Plot the graph .

The graph of the equation y2+12y=-x+1using graphing utility is shown below .

Here V is the vertex , and the line x=1494represents the directrix of the parabola .

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