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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

1-12 ■ Graphing Parabolas An equation of a parabola is given. (a) Find the vertex, focus, and directrix of the parabola. (b) Sketch a graph of the parabola and its directrix.

x = 1 2 y 2

To determine

(a)

To find:

The vertex, focus, and directrix of the parabola.

Explanation

Given:

The equation of parabola is,

x=12y2

Approach:

The following equation is the basic equation for an parabola that is not centered at the origin.

(xh)2=4p(yk) or (yk)2=4p(xh)

With the following properties,

Vertex V=(h,k) ……(1)

Focus F=(h,pk) or F=(ph,k) ……(2)

Directrix y=pk or x=ph ……(3)

Calculation:

Consider the equation,

x=12y2

Convert the above equation into equation of parabola.

y2=2x(y0)2=4(24)(x0)(y0)2=4(12)(x0)

Compare the equation of the parabola with the standard equation.

To determine

(b)

To sketch:

The graph of the parabola and its directrix.

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