Q. 18 Find the intercepts and graph ea... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 1: Q. 18 (page 24)

Find the intercepts and graph each equation by plotting points. Be sure to label the intercepts.
$y = - x^{2} + 1$ .

Short Answer

Expert verified

The intercepts are :

x-intercepts are $(- 1, 0)$ and $(1, 0)$ ,

y-intercept is $(0, 1)$ .

Step by step solution

Given information:

Consider the equation,

$y = - x^{2} + 1$ .

To find the x-intercept:

Let $y = 0$ in the equation,

Then, $- x^{2} + 1 = 0$

$(- 1) 脳 (- x^{2} + 1) = (- 1) 脳 0$ [Multiply by $(- 1)$ on both sides.]

$x^{2} - 1 = 0$

$(x + 1) (x - 1) = 0$ [Factors]

$x + 1 = 0$ or $x - 1 = 0$ [Zero Product Property]

$x = - 1$ or $x = 1$

The equation has two solutions, $- 1 a n d 1 .$

x - i n t e r c e p t s a r e (- 1, 0) a n d (1, 0) .

To find the y-intercept:

Let $x = 0$ in the equation,

Then, $y = 0 + 1$

$y = 1$

$y - i n t e r c e p t i s (0, 1)$ .

To draw the graph:

We can draw the graph of the equation $y = - x^{2} + 1$ by plotting the above intercepts and the points in the table below,

$x$	$y = - x^{2} + 1$	$(x, y)$
$- 3$	$- 8$	$(- 3, - 8)$
$- 2$	$- 3$	$(- 2, - 3)$
$2$	$- 3$	$(2, - 3)$
$3$	$- 8$	$(3, - 8)$

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91影视

Find the intercepts and graph each equation by plotting points. Be sure to label the intercepts.
$y = - x^{2} + 1$ .

Short Answer

Step by step solution

Given information:

To find the x-intercept:

To find the y-intercept:

To draw the graph:

One App. One Place for Learning.

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91影视

Find the intercepts and graph each equation by plotting points. Be sure to label the intercepts.y=-x2+1.

Short Answer

Step by step solution

Given information:

To find the x-intercept:

To find the y-intercept:

To draw the graph:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

Mechanics Maths

Applied Mathematics

Logic and Functions

Geometry

Study anywhere. Anytime. Across all devices.

Find the intercepts and graph each equation by plotting points. Be sure to label the intercepts.
$y = - x^{2} + 1$ .