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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 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

Find the real solutions of the equation $2 x^{2} + 7 x - 4 = 0$ .

In Problems 7鈥�22, solve each inequality.

$2 (2 x^{2} - 3 x) > - 9$

If $f (x) = x^{2} - 4$ , find $f (- 2) .$

If $p (x) = - x + 6,$ then

(a) Determine the slope and y-intercept of each function.

(b) Use the slope and y-intercept to graph the linear function.

(c) Determine the average rate of change of each function.

(d) Determine whether the linear function is increasing, decreasing, or constant.

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.

Hint: If necessary, write $f$ in the form $f (x) = a (x - h)^{2} + k$ .

$f (x) = \frac{2}{3} x^{2} + \frac{4}{3} x - 1$

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