Find the Factors and Roots of the Following Quadratic Equations and Identify Double Roots

Name______Date______Per_____AlgII Pre-AP

5.3-5.4 Review of Quadratic Functions

*Test will have a non-calculator portion which will require you to use factoring and completing the square methods.

Find the factors and roots of the following quadratic equations and identify double roots.

1. 2. 3.

4. 5. 6.

8. 9. 10.

11. 12. 13.

Find the solutions of the following quadratic functions by completing the square and rewrite in vertex form. Use simplified radical form for answer.

14. 15. 16.

17. A player bumps the volleyball with an initial velocity of 20 ft/s. This is modeled by , where h represents the height of the ball in feet in terms of the time t in seconds after the ball is hit.

a)  Complete the square to rewrite h in vertex form.

b)  Give the vertex and explain its meaning.

c)  How long before the ball lands?

d)  What was the balls initial height?

e)  How high is the ball after 1.2 seconds?

18) The path of a placekicked football can be modeled by the function where x is the horizontal distance (in yards) and y is the corresponding height (in yards). How far is the football kicked? What is the football’s maximum height? Justify your answer with a complete sentence.

19) A woodland jumping mouse hops along a parabolic path given by where x is the mouse’s horizontal position (in feet) and y is the corresponding height (in feet). Can the mouse jump over a fence that is 3 feet high? Explain. Justify your answer with a complete sentence.

20) A rectangular picnic site measures 24 feet by 10 feet. You want to double the sites are by adding the same distance to the length and the width.

a. Write an equation that you can solve to find the length and the width of the picnic site. Identify your variable.

b. Determine the dimensions of the of the picnic site. Justify your answer symbolically.

22. A city’s skate park is a rectangle 100 feet long by 50 feet wide. The city wants to triple the area of the skate park by adding the same distance to the length and the width.

a. Write an equation that you can solve to find the length and the width of the skate park. Identify your variable.

b. Determine the new dimensions of the of the skate park. Justify your answer symbolically.

22. The length of the longer leg of a right triangle is 2 meters less than the

hypotenuse. The shorter leg is 2 meters less than half as large as the longer

leg. Find the area of the right triangle.

Write the equations given the following roots:

23. 24.

25. 26.