# Solving Quadratics by Factoring and Graphing

Solve the quadratic equations in questions 1 - 5 by factoring.

1. x2 - 49 = 0

2. 3x3 - 12x = 0

3. 12x2 + 14x + 12 = 18

4. -x3 + 22x2 - 121x = 0

5. x2 - 4x = 5

In questions 6 - 10, solve the quadratic equation by graphing.

11. Write a quadratic equation that will have solutions of x = 3 and x = -7.

12. Write a quadratic equation that will have solutions of x = 12 and x = 2.

13. Write a quadratic equation that will have solutions of x = -1/2 and x = 4.

14. Write a quadratic equation that will have a solution of only x = 0.

15. Write a quadratic equation that has no solutions.

16. The product of two consecutive positive integers is 72. Find the integers.

17. The product of two consecutive negative integers is 10506. Write a quadratic equation that you could solve to find the integers.

18. A tennis ball is launched with an initial velocity of 24.5 m/s from the edge of a cliff that is 117.6 meters above the ground. Which quadratic equation could be used to correctly determine when the ball will hit the ground:

4.9t2 + 24.5t + 117.6 = 0

-4.9t2 - 24.5t + 117.6 = 0

-4.9t2 + 24.5t - 117.6 = 0

4.9t2 + 24.5t - 117.6 = 0

-4.9t2 + 24.5t + 117.6 = 0

19. Solve the equation you chose in question 18 to determine when the ball will hit the ground. (HINT: If you don't get one of the answers listed for this question, then maybe you chose the wrong equation in #18. Use this opportunity to double check your work!)

t = 8 seconds

t = 4 seconds

t = 3 seconds

t = -3 seconds

The ball will never reach the ground.

20. Using the same equation, determine when the ball is at a height of 49 meters.

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