Solve the problems below. Write the problem, the work, and the solution

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 - 9, state the solutions for the quadratic equation depicted in the graph.

6.

7.

8.

9.

10.Work backwards to make a quadratic equation that will have solutions ofx= 3 andx= -7.

11.Work backwards to make a quadratic equation that will have solutions ofx= 12 andx= 2.

12.Work backwards to make a quadratic equation that will have solutions ofx= -1/2 andx= 4.(Your equation must only have integer coefficients, meaning no fractions or decimals.)

13.make a quadratic equation that will have a solution of onlyx= 0. Note: this means there will be a double solution ofx= 0.

14.make a quadratic equation that cannot be factored.

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

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

17.make a quadratic equation to find two consecutive odd natural numbers whose product is 63.Then find the numbers.

18.A tennis ball is launched straight upward 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.