Chapter 1: Q. 22 (page 24)

Find the intercepts and graph each equation by plotting points. Be sure to label the intercepts.
$4 x^{2} + y = 4$ .

Short Answer

Expert verified

The intercepts are :

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

y-intercept is $(0, 4)$ .

Step by step solution

Given information:

Consider the equation,

$4 x^{2} + y = 4$ .

To find the x-intercept:

Let $y = 0$ in the equation,

Then, $4 x^{2} + 0 = 4$

$4 x^{2} = 4$

$\frac{4 x^{2}}{4} = \frac{4}{4}$ [Divide by 4 on both sides.]

$x^{2} = 1$

$x^{2} - 1 = 1 - 1$ [Add $- 1$ 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, $4 \times 0 + y = 4$

$y = 4$

$y - i n t e r c e p t i s (0, 4)$ .

To draw the graph:

We can draw the graph of the equation $4 x^{2} + y = 4$ by plotting the above intercepts and the points in the table below,

$x$	$y = 4 - 4 x^{2}$	$(x, y)$
$- 3$	$- 32$	$(- 3, - 32)$
$- 2$	$- 12$	$(- 2, - 12)$
$2$	$- 12$	$(2, 12)$
$3$	$- 32$	$(3, - 32)$

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Find the intercepts and graph each equation by plotting points. Be sure to label the intercepts.
$4 x^{2} + y = 4$ .

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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Find the intercepts and graph each equation by plotting points. Be sure to label the intercepts.4x2+y=4.

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

Geometry

Pure Maths

Applied Mathematics

Calculus

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Probability and Statistics

Study anywhere. Anytime. Across all devices.

Find the intercepts and graph each equation by plotting points. Be sure to label the intercepts.
$4 x^{2} + y = 4$ .