Chapter 5

Determine whether each function has a maximum or a minimum value and find the maximum or minimum value. Then state the domain and range of the function. $$ f(x)=x^{2}-10 x-1 $$

Solve each equation by using the method of your choice. Find exact solutions. \(4 x^{2}-8=0\)

Graph each inequality. $$ y \leq-x^{2}-3 x+10 $$

Solve each equation by completing the square. \(x^{2}+2 x-120=0\)

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. $$ x^{2}-2 x-1=0 $$

Solve each equation by factoring. Then graph. \(x^{2}+36=12 x\)

Determine whether each function has a maximum or a minimum value and find the maximum or minimum value. Then state the domain and range of the function. $$ f(x)=x^{2}+8 x+15 $$

Solve each equation by using the method of your choice. Find exact solutions. \(4 x^{2}+81=36 x\)

Graph each inequality. $$ y \geq-x^{2}-7 x+10 $$

Simplify. $$ (-2 i)(-6 i)(4 i) $$

Solve each equation by completing the square. \(x^{2}+2 x-6=0\)

For Exercises 30 and \(31,\) use the formula \(h(t)=v_{0} t-16 t^{2}\) where \(h(t)\) is the height of an object in feet, \(v_{0}\) is the object's initial velocity in feet per second, and \(t\) is the time in seconds. TENNIS A tennis ball is hit upward with a velocity of 48 feet per second. Ignoring the height of the tennis player, how long does it take for the ball to fall to the ground?

Solve each equation by factoring. Then graph. \(x^{2}+64=16 x\)

Determine whether each function has a maximum or a minimum value and find the maximum or minimum value. Then state the domain and range of the function. $$ f(x)=-x^{2}+12 x-28 $$

The average NFL salary \(A(t)\) (in thousands of dollars) can be estimated using \(A(t)=2.3 t^{2}-12.4 t+73.7,\) where \(t\) is the number of years since 1975. Determine a domain and range for which this function makes sense.

Graph each inequality. $$ y>-x^{2}+10 x-23 $$

Simplify. $$ 3 i(-5 i)^{2} $$

Solve each equation by completing the square. \(x^{2}-4 x+1=0\)

For Exercises 30 and \(31,\) use the formula \(h(t)=v_{0} t-16 t^{2}\) where \(h(t)\) is the height of an object in feet, \(v_{0}\) is the object's initial velocity in feet per second, and \(t\) is the time in seconds. BOATING A boat in distress launches a flare straight up with a velocity of 190 feet per second. Ignoring the height of the boat, how many seconds will it take for the flare to hit the water?

Find two consecutive even integers with a product of 224.

Determine whether each function has a maximum or a minimum value and find the maximum or minimum value. Then state the domain and range of the function. $$ f(x)=-14 x-x^{2}-109 $$

The average NFL salary \(A(t)\) (in thousands of dollars) can be estimated using \(A(t)=2.3 t^{2}-12.4 t+73.7,\) where \(t\) is the number of years since 1975. According to this model, in what year did the average salary first exceed one million dollars?

Graph each inequality. $$ y<-x^{2}+13 x-36 $$

Simplify. $$ i^{13} $$

Solve each equation by completing the square. \(2 x^{2}+3 x-5=0\)

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. $$ 2 x^{2}-3 x=9 $$

A rectangular photograph is 8 centimeters wide and 12 centimeters long. The photograph is enlarged by increasing the length and width by an equal amount in order to double its area. What are the dimensions of the new photograph?

ARCHITECTURE. For Exercises 32 and \(33,\) use the following information. The shape of each arch supporting the Exchange House can be modeled by \(h(x)=-0.025 x^{2}+2 x,\) where \(h(x)\) represents the height of the arch and \(x\) represents the horizontal distance from one end of the base in meters. Write the equation of the axis of symmetry and find the coordinates of the vertex of the graph of \(h(x) .\)

Graph each inequality. $$ y<2 x^{2}+3 x-5 $$

LAWN CARE For Exercises 33 and \(34,\) use the following information. The path of water from a sprinkler can be modeled by a quadratic function. The three functions below model paths for three different angles of the water. $$\begin{array}{l}{\text { Angle } \mathrm{A} : y=-0.28(x-3.09)^{2}+3.27} \\\ {\text { Angle } \mathrm{B} : y=-0.14(x-3.57)^{2}+2.39} \\ {\text { Angle } \mathrm{C} : y=-0.09(x-3.22)^{2}+1.53}\end{array}$$ Which sprinkler angle will send water the highest? Explain your reasoning.

Simplify. $$ i^{24} $$

Solve each equation by completing the square. \(2 x^{2}-3 x+1=0\)

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. $$ 4 x^{2}-8 x=5 $$

Solve each equation by factoring. \(3 x^{2}=5 x\)

ARCHITECTURE. For Exercises 32 and \(33,\) use the following information. The shape of each arch supporting the Exchange House can be modeled by \(h(x)=-0.025 x^{2}+2 x,\) where \(h(x)\) represents the height of the arch and \(x\) represents the horizontal distance from one end of the base in meters. According to this model, what is the maximum height of the arch?

Complete parts a–c for each quadratic equation. a. Find the value of the discriminant. b. Describe the number and type of roots. c. Find the exact solutions by using the Quadratic Formula. \(x^{2}+6 x=0\)

LAWN CARE For Exercises 33 and \(34,\) use the following information. The path of water from a sprinkler can be modeled by a quadratic function. The three functions below model paths for three different angles of the water. $$\begin{array}{l}{\text { Angle } \mathrm{A} : y=-0.28(x-3.09)^{2}+3.27} \\\ {\text { Angle } \mathrm{B} : y=-0.14(x-3.57)^{2}+2.39} \\ {\text { Angle } \mathrm{C} : y=-0.09(x-3.22)^{2}+1.53}\end{array}$$ Which sprinkler angle will send water the farthest? Explain your reasoning.

Simplify. $$ (5-2 i)+(4+4 i) $$

Solve each equation by completing the square. \(2 x^{2}+7 x+6=0\)

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. $$ 2 x^{2}=-5 x+12 $$

Solve each equation by factoring. \(4 x^{2}=-3 x\)

PHYSICS For Exercises \(34-36,\) use the following information. An object is fired straight up from the top of a 200 -foot tower at a velocity of 80 feet per second. The height \(h(t)\) of the object \(t\) seconds after firing is given by \(h(t)=-16 t^{2}+80 t+200\) What are the domain and range of the function? What domain and range values are reasonable in the given situation?

Complete parts a–c for each quadratic equation. a. Find the value of the discriminant. b. Describe the number and type of roots. c. Find the exact solutions by using the Quadratic Formula. \(4 x^{2}+7=9 x\)

Solve each inequality using a graph, a table, or algebraically. $$ 9 x^{2}-6 x+1 \leq 0 $$

LAWN CARE For Exercises 33 and \(34,\) use the following information. The path of water from a sprinkler can be modeled by a quadratic function. The three functions below model paths for three different angles of the water. $$\begin{array}{l}{\text { Angle } \mathrm{A} : y=-0.28(x-3.09)^{2}+3.27} \\\ {\text { Angle } \mathrm{B} : y=-0.14(x-3.57)^{2}+2.39} \\ {\text { Angle } \mathrm{C} : y=-0.09(x-3.22)^{2}+1.53}\end{array}$$ Which sprinkler angle will produce the widest path? The narrowest path?

Simplify. $$ (-2+i)+(-1-i) $$

Solve each equation by completing the square. \(9 x^{2}-6 x-4=0\)

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. $$ 2 x^{2}=x+15 $$

Solve each equation by factoring. \(4 x^{2}+7 x=2\)

PHYSICS For Exercises \(34-36,\) use the following information. An object is fired straight up from the top of a 200 -foot tower at a velocity of 80 feet per second. The height \(h(t)\) of the object \(t\) seconds after firing is given by \(h(t)=-16 t^{2}+80 t+200\) Find the maximum height reached by the object and the time that the height is reached.