Chapter 9

Solve by completing the square and round off the solutions to the nearest hundredth. $$(3 x-2) 2=5-15 x$$

Use the quadratic formula to solve the following. $$(3 x+4)(3 x-1)-33 x=-20$$

Determine the x- and y-intercepts. $$ y=-x 2+10 x-25 $$

Solve using the quadratic formula. $$ -8 x_{2}+20 x-13=0 $$

To safely use a ladder, the base should be placed about \(1 / 4\) of the ladder's length away from the wall. If a 20-foot ladder is to be safely used, then how high against a building will the top of the ladder reach? Round off to the nearest hundredth.

The value in dollars of a new car is modeled by the formula \(V(t)=125 t 2-3,000 t+22,000,\) where \(t\) represents the number of years since it was purchased. Determine the minimum value of the car.

Solve by completing the square and round off the solutions to the nearest hundredth. $$(2 x+1)(3 x+1)=9 x+4$$

Use the quadratic formula to solve the following. $$27 y(y+1)+2(3 y-2)=0$$

Find the vertex and the line of symmetry. $$ y=x 2-6 x+1 $$

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

Solve and round off the solutions to the nearest hundredth. $$ 9 x(x+2)=18 x+1 $$

The diagonal of a television monitor measures 32 inches. If the monitor has a 3: 2 aspect ratio, then determine its length and width. Round off to the nearest hundredth.

Solve by completing the square and round off the solutions to the nearest hundredth. $$(3 x+1)(4 x-1)=17 x-4$$

Use the quadratic formula to solve the following. $$8(4 y 2+3)-3(28 y-1)=0$$

The diagonal of a television monitor measures 52 inches. If the monitor has a 16:9 aspect ratio, then determine its length and width. Round off to the nearest hundredth. Business Problems

The area of a certain rectangular pen is given by the formula \(A=14 w-w_{2},\) where \(w\) represents the width in feet. Determine the width that produces the maximum area.

Solve by completing the square and round off the solutions to the nearest hundredth. $$9 x(x-1)-2(2 x-1)=-4 x$$

Find the vertex and the line of symmetry. $$ y=x 2+3 x-1 $$

Solve using the quadratic formula. $$ 2 x_{2}+3 x+2=0 $$

Solve and round off the solutions to the nearest hundredth. $$ (x+3)(x-7)=11-4 x $$

The profit in dollars of running an assembly line that produces custom uniforms each day is given by the function \(P(t)=-40 t 2+960 t-4,000,\) where \(t\) represents the number of hours the line is in operation. a. Calculate the profit on running the assembly line for 10 hours a day. b. Calculate the number of hours the assembly line should run in order to break even. Round off to the nearest tenth of an hour.

Determine the vertex. $$ y=-(x-5) 2+3 $$

Solve by completing the square and round off the solutions to the nearest hundredth. $$(6 x+1) 2-6(6 x+1)=0$$

Use the quadratic formula to solve the following. $$(x+3) 2-10(x+5)=-2(x+1)$$

Solve using the quadratic formula. $$ 4 x_{2}+2 x+1=0 $$

Solve and round off the solutions to the nearest hundredth. $$ (x-4)(x-3)=66-7 x $$

Research and discuss the Hindu method for completing the square.

When talking about a quadratic equation in standard form, \(a x 2+b x+c=0\), why is it necessary to state that \(a \neq 0\) ? What happens if \(a\) is equal to 0 ?

Graph. Find the vertex and the y-intercept. In addition, find the x-intercepts if they exist. $$ y=x 2+8 x+12 $$

Solve and round off the solutions to the nearest hundredth. $$ (x-2) 2=67-4 x $$

\(.\) If \(\$ 1,200\) is invested in an account earning an annual interest rate \(r,\) then the amount \(A\) that is in the account at the end of 2 years is given by the formula \(A=1,200(1+r) 2\). If at the end of 2 years the amount in the account is \(\$ 1,335.63,\) then what was the interest rate?

Research and discuss the history of the quadratic formula and solutions to quadratic equations.

Graph. Find the vertex and the y-intercept. In addition, find the x-intercepts if they exist. $$ y=-x 2-6 x+7 $$

Solve and round off the solutions to the nearest hundredth. $$ (x+3) 2=6 x+59 $$

A manufacturing company has determined that the daily revenue, \(R\), in thousands of dollars depends on the number, \(n\), of palettes of product sold according to the formula \(R=12 n-0.6 n 2 .\) Determine the number of palettes that must be sold in order to maintain revenues at \(\$ 60,000\) per day.

Solve using the quadratic formula. $$ 2 x(x-1)=-1 $$

Solve and round off the solutions to the nearest hundredth. $$ (2 x+1)(x+3)-(x+7)=(x+3) 2 $$

The height of a projectile launched upward at a speed of 32 feet/second from a height of 128 feet is given by the function \(h(t)=-16 t_{2}+32 t+128 .\) a. What is the height of the projectile at \(1 / 2\) second? b. At what time after launch will the projectile reach a height of 128 feet?

Graph. Find the vertex and the y-intercept. In addition, find the x-intercepts if they exist. $$ y=x 2+4 x $$

Solve using the quadratic formula. $$ x(2 x+5)=3 x-5 $$

Solve and round off the solutions to the nearest hundredth. $$ (3 x-1)(x+4)=2 x(x+6)-(x-3) $$

The height of a projectile launched upward at a speed of 16 feet/second from a height of 192 feet is given by the function \(h(t)=-16 t_{2}+16 t+192\). a. What is the height of the projectile at \(3 / 2\) seconds? b. At what time will the projectile reach 128 feet?

Determine the vertex. $$ y=(x+2) 2-5 $$

Graph. Find the vertex and the y-intercept. In addition, find the x-intercepts if they exist. $$ y=4 x 2-4 x+1 $$

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

Set up an algebraic equation and use it to solve the following. If 9 is subtracted from 4 times the square of a number, then the result is 3 . Find the number.

The height of an object dropped from the top of a 144 -foot building is given by \(h(t)=-16 t 2+144 .\) How long will it take to reach a point halfway to the ground?

Rewrite in \(y=a(x-h)_{2}+k\) form and determine the vertex. $$ y=x_{2}-14 x+24 $$

Solve using the quadratic formula. $$ 5 t(t-1)=t-4 $$

Set up an algebraic equation and use it to solve the following. If 20 is subtracted from the square of a number, then the result is \(4 .\) Find the number.