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Chapter 3: Q .6 (page 176)

Graph the equation $x^{2} + y^{2} - 4 x + 8 y - 5 = 0$ .

Short Answer

Expert verified

The required graph is

Step by step solution

01

Step 1. Given information.

Graph the equation $x^{2} + y^{2} - 4 x + 8 y - 5 = 0$ .

02

Step 2. Compare with equation of circle.

Equation of circle is:

${(x - p)}^{2} + {(y - q)}^{2} = r^{2}$

$(p, q)$ is the center of the circle, r is theradius.

Lets write $x^{2} + y^{2} - 4 x + 8 y - 5 = 0$ in this form ${(x - p)}^{2} + {(y - q)}^{2} = r^{2}$ .

$x^{2} + y^{2} - 4 x + 8 y - 5 = 0 x^{2} - 4 x + y^{2} + 8 y - 5 = 0 {(x - 2)}^{2} - 4 + {(y + 4)}^{2} - 16 - 5 = 0 {(x - 2)}^{2} + {(y + 4)}^{2} = 25$

So, the center of circle has coordinates $(2, - 4)$ and the radius is 5.

03

Step 3. Plot the graph of circle.

Plot the graph of circle ${(x - 2)}^{2} + {(y + 4)}^{2} = 25$ .

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Most popular questions from this chapter

Why does the graph of a quadratic function open up if $a > 0$ and down if $a < 0$ ?

Graph $y = 2 x - 3 .$

Graph the function $f$ by starting with the graph of $y = x^{2}$ and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility.

$f (x) = (x + 2)^{2} - 2$

The monthly revenue R achieved by selling

x wristwatches is figured to be $R (x) = 75 x - 0.2 x^{2}$ The monthly cost C of selling x wristwatches is $C (x) = 32 x + 1750$

(a) How many wristwatches must the firm sell to maximize revenue? What is the maximum revenue?

(b) Profit is given as P(x) = R(x) - C(x). What is the profit function?

(c) How many wristwatches must the firm sell to maximize

profit? What is the maximum profit?

(d) Provide a reasonable explanation as to why the answers found in parts (a) and (c) differ. Explain why a quadratic function is a reasonable model for revenue.

In the United States, the birthrate B of unmarried women (births per 1000 unmarried women) for women whose age is a is modeled by the function

$B (a) = - 0.27 a^{2} + 14.23 a - 120.16$

(a) What is the age of unmarried women with the highest birthrate?

(b) What is the highest birthrate of unmarried women?

(c) Evaluate and interpret B(40).

See all solutions

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