Quadratics Review

Factoring

100

Factor.

x²+11x+24

(x+3)(x+8)

200

Factor.

x²−12x+20

(x-2)(x-10)

300

Factor.

3x²−20x−7

(3x+1)(x-7)

400

Factor.

5x²−2x−3

(5x+3)(x-1)

500

Factor.

−3x²+9x+30

-3(x+2)(x-5)

Imaginary/Complex Numbers

100

Write √(5) in simplest radical form.

i√(5)

200

Write √(−147) in simplest radical form.

7i√(3) 

300

Simplify the expression to a + bi form: 

(−10+7i)+(−3+4i)

−13+11i

400

Simplify the expression to a + bi form: 

(6+9i)−(−3−i)

9+10i

500

Simplify the expression to a + bi form:

(7+9i)(7+4i)

13+91i

Solving Quadratics

100

Solve for all values of x by factoring.

x²−4x=4x

x=0

x=8

200

Solve the following quadratic equation for all values of x in simplest form.

9x²-108=-8

x=10/3

x=-10/3

300

Solve the equation for all values of x by completing the square.

x²+12x+23=0

x=-6+√(13)

x=-6-√(13)  

400

Use the quadratic formula to solve. Express your answer in simplest form.

25x²+36x+9=6x

x=-3/5

x=-3/5

500

Solve the equation for all values of x. (You choose the method)

x²−45=4x

x=-5

x=9

Solving Quadratics

100

Solve for all values of x by factoring.

x²−9x−20= −2x−2

x=−2

x=9

200

Solve the following quadratic equation for all values of x in simplest form.

18−x²=13

x=√(5)

x=-√(5)  

300

Solve the equation for all values of x by completing the square.

2x²−32x=-120

x=6

x=10

400

Use the quadratic formula to solve. Express your answer in simplest form. 

−x²−3x−13=−2x²

x=3±√(61)/2

500

Solve the equation for all values of x. (You choose the method)

5x²+28x−2=7x−6

x=-4

x=-1/5

Word Problems

100

The width of a rectangle is the length minus 8 units. The area of the rectangle is 9 square units. What is the length, in units, of the rectangle?

length=9

200

An object is launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. What will be the object's maximum height? When will it attain this height?

h(t) = –16t² + 64t + 80

Max height = 144 feet

It will attain 144 feet at 2 seconds 

300

The length of a rectangle is the sum of the width and 4. The area of the rectangle is 32 square units. What is the width, in units, of the rectangle?

width=4

400

An object is launched from ground level directly upward at 56 m/s. At what time(s) is the object at a height of 40 meters?

h(t) = –16t² + 39.2t

 1 second and 2.5 seconds

500

An object is launched at 19.6 meters per second (m/s) from a 58.8-meter-tall platform. The equation for the object's height, h, at time, t, seconds after launch is

h(t) = –4.9t² + 19.6t + 58.8

What is the height of the object at 2 seconds?

78.4 meters