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Homework Quadratic Formula and Discriminant
Solve each equation using the Quadratic Formula. Leave your answer in simplest
radical form. If the answer is complex, find the simplified form as well.
1. x2  4x + 3 = 0
2. 2x2 + 3x  4 = 0
4. x2 + 3x =3
5. 4x2 + 3 = 9x
3. 8x2  2x  5 = 0
6. 2x – 5 = –x2
7. Your school sells yearbooks every spring. The total profit p made depends on the
amount x the school charges for each yearbook. The profit is modeled by the
equation p = 2x2 + 70x + 520. What is the smallest amount in dollars the school can
charge for a yearbook and make a profit of at least $1000?
8. Engineers can use the formula d = 0.05s2 + 1.1s to estimate the minimum stopping
distance d in feet for a vehicle traveling s miles per hour. Solve using the quadratic
formula.
a. If a car can stop after 65 feet, what is the fastest it could have been traveling when
the driver put on the brakes?
b. Reasoning Explain how you knew which of the two solutions from the
Quadratic Formula to use. (Hint: Remember this is a real situation.)
9. Reasoning Explain why a quadratic equation has no real solutions if the
discriminant is less than zero.
Evaluate the discriminant for each equation. Determine the number of real
solutions.
10. 12x2 + 5x + 2 = 0
11. x2 x + 6 = 0
12. 2x  5 = x2
13. 4x2 + 7 = 9x
14. x2  4x = 4
15. 3x + 6 = 6x2
Solve each equation using any method. Use completing the square, factoring and
the quadratic formula all at least once.
16. 7x2 + 3x = 12
17. x2 + 6x  7 = 0
18. 5x =–3x2 + 2
19. 12x + 7 = 5  2x2
20. 9x2  6x  4 = 5
21. 2x  24 = x2
Without graphing, determine how many x-intercepts each function has. (Use the
discriminant)
22. y = 2x2  3x + 5
23. y = 2x2  4x + 1
24. y = x2 + 3x + 3
25. y = 9x2  12x + 7
26. y = 5x2+ 8x  3
27. y = x2 + 16x + 64