Chapter 9

The height of a projectile shot straight up into the air at 80 feet/second from the ground is given by \(h(t)=-16 t 2+80 t\). At what time will the projectile reach 95 feet? Part D: Discussion Board

Rewrite in \(y=a(x-h)_{2}+k\) form and determine the vertex. $$ y=x 2-12 x+40 $$

Graph. Find the vertex and the y-intercept. In addition, find the x-intercepts if they exist. $$ y=-2 x 2+8 x-7 $$

Solve using the quadratic formula. $$ (2 x+3) 2=16 x+4 $$

Set up an algebraic equation and use it to solve the following. If 1 is added to 3 times the square of a number, then the result is 2 . Find the number.

Discuss the strategy of always using the quadratic formula to solve quadratic equations.

Rewrite in \(y=a(x-h)_{2}+k\) form and determine the vertex. $$ y=x 2+4 x-12 $$

Solve using the quadratic formula. $$ (2 y+5) 2-12(y+1)=0 $$

Set up an algebraic equation and use it to solve the following. If 3 is added to 2 times the square of a number, then the result is 12 . Find the number.

Rewrite in \(y=a(x-h)_{2}+k\) form and determine the vertex. $$ y=x 2+6 x-1 $$

Determine the maximum or minimum \(y\) -value. \(y=x 2-10 x+1\)

Solve using the quadratic formula. $$ -3(y+3)(y-5)=5 y+46 $$

Set up an algebraic equation and use it to solve the following. If a square has an area of 8 square centimeters, then find the length of each side.

Determine the maximum or minimum \(y\) -value. \(y=-x 2+12 x-1\)

Solve using the quadratic formula. $$ -2(y-4)(y+1)=3 y+10 $$

Set up an algebraic equation and use it to solve the following. If a circle has an area of \(32 \pi\) square centimeters, then find the length of the radius.

Rewrite in \(y=a(x-h)_{2}+k\) form and determine the vertex. $$ y=3 x_{2}-6 x+5 $$

Determine the maximum or minimum \(y\) -value. \(y=-5 x 2+6 x\)

Solve using the quadratic formula. $$ 9 x(x-1)+3(x+2)=1 $$

Determine the maximum or minimum \(y\) -value. $$ y=2 x 2-x-1 $$

Solve using the quadratic formula. $$ 5 x(x+2)-6(2 x-1)=5 $$

Set up an algebraic equation and use it to solve the following. The surface area of a sphere is \(75 \pi\) square centimeters. Find the radius of the sphere. (The surface area of a sphere is given by \(S A=4 \pi r 2 .\)

The value in dollars of a new car is modeled by the function V(t)=125t2?3,000t+22,000, where t represents the number of years since it was purchased. Determine the age of the car when its value is at a minimum.

Solve using the quadratic formula. $$ 3(t-1)-2 t(t-2)=6 t $$

Set up an algebraic equation and use it to solve the following. The length of a rectangle is 6 times its width. If the area is 96 square inches, then find the dimensions of the rectangle.

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. What is the maximum height of the baseball?

Solve using the quadratic formula. $$ 3(t-3)-t(t-5)=7 t $$

Set up an algebraic equation and use it to solve the following. The base of a triangle is twice its height. If the area is 16 square centimeters, then find the length of its base.

Rewrite in terms of \(i\). $$ -36--\sqrt{1} $$

Solve using the quadratic formula. $$ (2 x+3)(2 x-3)-5(x 2+1)=-9 $$

Set up an algebraic equation and use it to solve the following. A square has an area of 36 square units. By what equal amount will the sides have to be increased to create a square with double the given area?

Graph. $$ y=(x-1) 2 $$

Solve using the quadratic formula. $$ 5(x+1)(x-1)-3 x 2=-8 $$

A circle has an area of \(25 \pi\) square units. By what amount will the radius have to be increased to create a circle with double the given area?

If the sides of a square measure 1 unit, then find the length of the diagonal.

Research and discuss the rich history of imaginary numbers.

If the sides of a square measure 2 units, then find the length of the diagonal.

Perform the operation. $$ (2-5 i)+(3+4 i) $$

Research and discuss real-world applications involving complex numbers.

The diagonal of a square measures 5 inches. Find the length of each side.

Perform the operation. $$ (6-7 i)-(12-3 i) $$

The diagonal of a square measures 3 inches. Find the length of each side.

Perform the operation. $$ (2-3 i)(5+i) $$

The length of a rectangle is twice its width. If the diagonal measures 10 feet, then find the dimensions of the rectangle.

The length of a rectangle is twice its width. If the diagonal measures 8 feet, then find the dimensions of the rectangle.

Solve. $$ 9 x_{2}+25=0 $$

The length of a rectangle is 3 times its width. If the diagonal measures 5 meters, then find the dimensions of the rectangle.

The length of a rectangle is 3 times its width. If the diagonal measures 2 feet, then find the dimensions of the rectangle.

Solve. $$ y 2-y+5=0 $$

The height in feet of an object dropped from a 9-foot ladder is given by \(h(t)=-16 t 2+9,\) where \(t\) represents the time in seconds after the object has been dropped. How long does it take the object to hit the ground? (Hint: The height is 0 when the object hits the ground.)