91Ó°ÊÓ

Solve the quadratic equation by completing the square. $$ x^{2}-2 x-3=0 $$

In Exercises 79-84, evaluate the expression for each value of \(x\). (If not possible, state the reason.) \(\frac{x}{x+2}\) (a) \(x=2\) (b) \(x=-2\)

The number of lumens (time rate of flow of light) \(L\) from a fluorescent lamp can be approximated by the model $$ L=-0.294 x^{2}+97.744 x-664.875, \quad 20 \leq x \leq 90 $$ where \(x\) is the wattage of the lamp. (a) Use a graphing utility to graph the function. (b) Use the graph from part (a) to estimate the wattage necessary to obtain 2000 lumens.

\(f(x)=\sqrt{5 x}, \quad \frac{f(x)-f(5)}{x-5}, x \neq 5\)

Identify any relationships that exist among the lines, and then use a graphing utility to graph the three equations in the same viewing window. Adjust the viewing window so that the slope appears visually correct-that is, so that parallel lines appear parallel and perpendicular lines appear to intersect at right angles. (a) \(y=2 x\) (b) \(y=-2 x\) (c) \(y=\frac{1}{2} x\)

In Exercises 85-96, identify the rule(s) of algebra illustrated by the statement. \(x+9=9+x\) 86\. \(2\left(\frac{1}{2}\right)=1\)

Write the standard form of the equation of the circle with the given characteristics. Center: \((2,-1)\); radius: 4

Solve the quadratic equation by completing the square. $$ x^{2}+12 x+25=0 $$

True or False? In Exercises 85 and 86, determine whether the statement is true or false. Justify your answer. $$ \text { If } f \text { is an even function, } f^{-1} \text { exists. } $$

Write the standard form of the equation of the circle with the given characteristics. Center: \((-7,-4)\); radius: 7