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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 2: Q. 1 (page 76)

The intercepts of the equation $x^{2} + 4 y^{2} = 16$ are ______________________________.

Short Answer

Expert verified

The intercepts are $(4, 0), (- 4, 0), (0, 2) and (0, - 2)$ .

Step by step solution

01

Step 1. Given information

The given equation is $x^{2} + 4 y^{2} = 16$ .

Need to find the intercepts of the given equation.

02

Step 2. Finding y-intercept

Substitute $x = 0$ in the equation $x^{2} + 4 y^{2} = 16$ and solve for yto obtain the y-intercepts.

$\begin{array}{rcl} {(0)}^{2} + 4 {(y)}^{2} & = & 16 \\ 4 y^{2} & = & 16 \\ y^{2} & = & 4 \\ y^{2} - 4 & = & 0 \\ (y - 2) (y + 2) & = & 0 \end{array}$

$y = 2 o r y = - 2$

The intercepts on the y-axis are $(0, 2)$ and $(0, - 2)$ .

03

Step 3. Finding x-intercept

Substitute $y = 0$ in the equation $x^{2} + 4 y^{2} = 16$ and solve for $x$ to obtain the x-intercepts.

$\begin{array}{rcl} x^{2} + 4 {(0)}^{2} & = & 16 \\ x^{2} & = & 16 \\ x^{2} - 16 & = & 0 \\ (x - 4) (x + 4) & = & 0 \end{array}$

$\begin{array}{rcl} x & = & 4 o r x = - 4 \end{array}$

The intercepts on the x-axis are $(4, 0)$ and $(- 4, 0)$ .

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Most popular questions from this chapter

True or False

The graph of $y = - f (x)$ is the reflection about the $x$ -axis of the graph of $y = f (x)$ .

The intercepts of the equation $y = x^{2} - 9$ are

A wire $10$ meters long is to be cut into two pieces. One piece will be shaped as an equilateral triangle, and the other piece will be shaped as a circle.

Part (a): Express the total area Aenclosed by the pieces of wire as a function of the length x of a side of the equilateral triangle.

Part (b): What is the domain of A?

Part (c): Graph $A = A (x)$ . For what value of xis Asmallest?

A rectangle has one corner in quadrant I on the graph of $y = 16 - x^{2}$ , another at the origin, a third on the positive y-axis and the fourth on the positive x-axis. See the figure.

Part (a): Express the area Aof the rectangle as a function of x.

Part (b): What is the domain of A?

Part (c): Graph $A = A (x)$ . For what value of xis Alargest?

In Problems 7鈥�18, match each graph to one of the following functions:

$A . y = x^{2} + 2 B . y = - x^{2} + 2 C . y = |x| + 2 D . y = - |x| + 2 E . y = {(x - 2)}^{2} F . y = - {(x + 2)}^{2} G . y = |x - 2| H . y = - |x + 2| I . y = 2 x^{2} J . y = - 2 x^{2} K . y = 2 |x| L . y = - 2 |x|$

See all solutions

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