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Mathorio

Worksheet

The Quadratic Formula

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Show your work for each problem.

1.
In the equation , what are the values of , , and ?
1. a), ,
2. b), ,
3. c), ,
4. d), ,
2.
Calculate the discriminant for .
3.
If the discriminant , how many real solutions does the equation have?
1. a)One solution
2. b)Two solutions
3. c)Three solutions
4. d)No real solutions
4.
What is if ?
5.
Solve using the quadratic formula.
6.
Calculate the discriminant for .
7.
What does it mean if the discriminant ?
1. a)The equation has no solutions
2. b)The equation cannot be solved
3. c)The equation has exactly one real solution (double root)
4. d)The equation has two different solutions
8.
Solve using the quadratic formula.
9.
Which equation has no real solutions?
1. a)
2. b)
3. c)
4. d)
10.
Solve using the quadratic formula.
11.
Solve . Enter the positive solution as a fraction (e.g., 5/3).
12.
A ball is thrown upward with height meters. When does it hit the ground?
13.
What are the solutions to ?
1. a)
2. b)
3. c)
4. d)
14.
For what value of does have exactly one solution?
15.
Solve and verify by factoring.