Chapter 9

The area of a triangle is 14 square feet. If the base is 4 feet more than 2 times the height, then find the length of the base and the height.

Use the quadratic formula to solve the following. $$3 x_{2}+6 x+1=8$$

Solve using any method. $$ x(x-5)=12 $$

Solve using the quadratic formula. $$ x 2+2 x+9=0 $$

The area of a triangle is 8 square meters. If the base is 4 meters less than the height, then find the length of the base and the height.

Solve using any method. $$ (x+1)(x-8)+28=3 x $$

Solve by completing the square. $$3 x_{2}+2 x-2=0$$

Use the quadratic formula to solve the following. $$-2 y_{2}=3(y-1)$$

Solve using the quadratic formula. $$ y 2-6 y+17=0 $$

The perimeter of a rectangle is 54 centimeters and the area is 180 square centimeters. Find the dimensions of the rectangle.

Given the following quadratic functions, determine the domain and range. $$ f(x)=3 x 2+30 x+50 $$

Use the quadratic formula to solve the following. $$3 y_{2}=5(2 y-1)$$

Solve using any method. $$ (9 x-2)(x+4)=28 x-9 $$

Solve using the quadratic formula. $$ y 2-2 y+19=0 $$

Solve by extracting the roots. $$ 2(3 y-13) 2-52=0 $$

The perimeter of a rectangle is 50 inches and the area is 126 square inches. Find the dimensions of the rectangle.

Given the following quadratic functions, determine the domain and range. $$ f(x)=3 x 2+30 x+50 $$

Solve by completing the square. $$x(x+1)-11(x-2)=0$$

Set up an algebraic equation and use it to solve. The length of a rectangle is 2 inches less than twice the width. If the area measures 25 square inches, then find the dimensions of the rectangle. Round off to the nearest hundredth.

Use the quadratic formula to solve the following. $$(t+1) 2=2 t+7$$

Solve using the quadratic formula. $$ t 2-5 t+10=0 $$

Find a quadratic equation in standard form with the following solutions. $$ \pm 7 $$

George maintains a successful 6-meter-by-8-meter garden. Next season he plans on doubling the planting area by increasing the width and height by an equal amount. By how much must he increase the length and width?

Solve by completing the square. $$(x+1)(x+7)-4(3 x+2)=0$$

Use the quadratic formula to solve the following. $$(2 t-1) 2=73-4 t$$

Set up an algebraic equation and use it to solve. An 18-foot ladder leaning against a building reaches a height of 17 feet. How far is the base of the ladder from the wall? Round to the nearest tenth of a foot.

Solve using the quadratic formula. $$ t 2+3 t+4=0 $$

Find a quadratic equation in standard form with the following solutions. $$ \pm 13 $$

A uniform brick border is to be constructed around a 6 -foot-by-8-foot garden. If the total area of the garden, including the border, is to be 100 square feet, then find the width of the brick border. P

Given the following quadratic functions, determine the domain and range. $$ g(x)=-7 x 2-14 x-9 $$

Solve by completing the square. $$y 2=(2 y+3)(y-1)-2(y-1)$$

Use the quadratic formula to solve the following. $$(x+5)(x-1)=2 x+1$$

Set up an algebraic equation and use it to solve. The value in dollars of a new car is modeled by the function \(V(t)=125 t 2-3,000 t+22,000,\) where \(t\) represents the number of years since it was purchased. Determine the age of the car when its value is $$\$ 22,000$$.

Solve by completing the square. $$(2 y+5)(y-5)-y(y-8)=-24$$

Use the quadratic formula to solve the following. $$(x+7)(x-2)=3(x+1)$$

Set up an algebraic equation and use it to solve. The height in feet reached by a baseball tossed upward at a speed of 48 feet/second from the ground is given by the function \(h(t)=-16 t 2+48 t\), where \(t\) represents time in seconds. At what time will the baseball reach a height of 16 feet?

The height of a projectile launched straight up from a mound is given by the function \(h(t)=-16 t 2+96 t+4,\) where \(t\) represents seconds after launch. What is the maximum height?

Solve by completing the square. $$(t+2) 2=3(3 t+1)$$

Use the quadratic formula to solve the following. $$x(x+5)=3(x-1)$$

Determine the x- and y-intercepts. $$ y=2 x 2+5 x-3 $$

Solve using the quadratic formula. $$ -y 2-y-2=0 $$

The profit in dollars generated by producing and selling \(x\) custom lamps is given by the function \(P(x)=-10 x_{2}+800 x-12,000 .\) What is the maximum profit?

Solve by completing the square. $$(3 t+2)(t-4)-(t-8)=1-10 t$$

Use the quadratic formula to solve the following. $$x(x+4)=-7$$

Determine the x- and y-intercepts. $$ y=x 2-12 $$

The revenue in dollars generated from selling a particular item is modeled by the formula \(R(x)=100 x-0.0025 x_{2},\) where \(x\) represents the number of units sold. What number of units must be sold to maximize revenue?

Use the quadratic formula to solve the following. $$(5 x+3)(5 x-3)-10(x-1)=0$$

Solve by completing the square and round off the solutions to the nearest hundredth. $$(2 x-1) 2=2 x$$

Solve using the quadratic formula. $$ -2 x_{2}+10 x-17=0 $$

The top of a 20-foot ladder, leaning against a building, reaches a height of 18 feet. How far is the base of the ladder from the wall? Round off to the nearest hundredth.