The Discriminant

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Show your work for each problem.

1.
What is the discriminant formula for ?
1. a)
2. b)
3. c)
4. d)
2.
If the discriminant is positive (), how many real solutions does the equation have?
1. a)Three real solutions
2. b)Two distinct real solutions
3. c)One real solution
4. d)No real solutions
3.
Calculate the discriminant for .
4.
Calculate the discriminant for .
5.
A quadratic equation has discriminant . What does this tell us?
1. a)No real solutions
2. b)Four real solutions
3. c)One real solution
4. d)Two real solutions
6.
Calculate the discriminant for .
7.
Calculate the discriminant of and determine the nature of solutions.
8.
The parabola has its vertex above the x-axis. What can you conclude about the discriminant?
1. a)Cannot determine
2. b)
3. c)
4. d)
9.
Find the discriminant of and interpret the result.
10.
How many real solutions does have? (Answer: 0, 1, or 2)
11.
For what value of does have exactly one solution?
12.
For what values of does have two distinct real solutions? (Enter as inequality, e.g., m > 5 or m < -5)
13.
A ball is thrown upward with height meters. Use the discriminant to determine if it reaches 50 meters.
14.
The equation has no real solutions. Which of these could be ?
1. a)
2. b)
3. c)
4. d)
15.
Find all values of for which has exactly one solution.