   Chapter 10.1, Problem 7E

Chapter
Section
Textbook Problem

# Sketching a Parabola In Exercises 7–14, find the vertex, focus, and directrix of the parabola, and sketch its graph. y 2 = − 8 x

To determine

To graph: The parabola y2=8x and also find its vertex, focus and directrix.

Explanation

Given:

The provided equation of parabola is:

y2=8x

Graph:

Consider the provided equation of parabola:

y2=8x

Now, the standard equation of a parabola with vertex (h,k) and directrix x=hp on a horizontal axis is given by:

(yk)2=4p(xh) …… (1)

And the coordinates of focus are:

(h+p,k)

Now compare equation (1) with the provided equation of parabola:

y2=8x(y0)2=4(2)(x0)

Value of k is 0, value of p is 2 and value of h is 0.

Thus, substitute 0 for h, 2 for p and 0 for k, the focus of the provided parabola is (2,0).

And also, since h=0 and k=0, the vertex of the parabola is (0,0)

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