Solving by Factoring
Solving by Completing the Square
Solving by Quadratic Formula
Application Problems
Grab Bag
100
Solve the following quadratic equation by factoring:
(3x-1)(x+7)=0
x = ⅓ and -7
100
Solve the following quadratic equation by completing the square: x2 - 4x - 5 = 0
x = -1 and 5
100
Solve the following quadratic equation by using the quadratic formula: x2 + 2x - 8 = 0
x = -4 and 2
100
The product of two consecutive positive even integers is 288
What is 16 and 18
100
Factor the following quadratic expression:
x2 - 3x - 4
(x - 4)(x + 1)
200
Solve the following quadratic equation by factoring:
x2 - 3x - 4 = 0
x = -1 and 4
200
Solve the following quadratic equation by completing the square: x2 + 6x - 7 = 9
x = -8 and 2
200
Solve the following quadratic equation by using the quadratic formula: x2 + 5x - 4 = 2
x = -6 and 1
200
A rectangular picture has a height that is 3in less than its width. Its area is of the picture is 40 square inches. What are the dimensions of the picture?
5 in and 8 in
200
Determine the mistake in the following equations. Explain the correct way to solve the equation: 
Did not do "-b" at the beginning of the problem. The work should have a positive 9 rather than negative. The answer would be 4 and 5.
300
Solve the following quadratic equation by factoring:
x2 + 12 = 7x
x = 3 and 4
300
Solve the following quadratic equation by completing the square: x2 - 12x + 23 = 0
x = 
300
Solve the following quadratic equation by using the quadratic formula: 2x2 - x - 9 = - 3
x = 2 and 
300
In a right triangle, the length of the longer leg is 2 more inches than the shorter leg. The length of the hypotenuse is 4 more inches than the length of the shorter leg. Find all three side lengths. (Hint: a2 + b2 = c2)
6 in, 8 in, and 10 in.
300
Factor the following quadratic expression:
3x2 - 11x + 6
(3x - 2)(x - 3)
400
Solve the following quadratic equation by factoring:
2x2 - 7x + 3 = 0
x = ½ and 3
400
Solve the following quadratic equation by completing the square: 6x2 - 48 = -12x
x = -4 and 2
400
Solve the following quadratic equation by using the quadratic formula: x2 + x - 4 = 0
400
In a right triangle, the length of the shorter leg is 7 less inches than the longest leg. The length of the hypotenuse is 1 inch longer than the length of the longest leg. Find all three side lengths. (Hint: a2 + b2 = c2)
5 in, 12 in, and 13 in.
400
Determine the mistake in the following equations. Explain the correct way to solve the equation:
They factored incorrectly. It should have been (x-1) instead of (x+1). The final answer should be 
500
Solve the following quadratic equation by factoring:
39x + 45 = - 6x2
x = -5 and -1½
500
Solve the following quadratic equation by completing the square: 3x2 - 30x + 78 = 24
x = 
500
Solve the following quadratic equation by using the quadratic formula: 2n2 + 39 = - 18n
500
A rectangular trenching shovel, as its name depicts, is used to dig trenches. Most trenching shovels have a length that is 5 more than 3 times the width. Its area of the surface is 50 square inches. What are the dimensions of the shovel?
and 15 in.500
A rectangular garden has a length that is 3ft less than twice its width. Its area is of the garden is 20 square feet. What are the dimensions of the garden?
4 feet and 5 feet