Quadratics Test Review Name: Pd:

Work out answers on another sheet of paper. This review is due on the day of the test and will be a quiz grade. No work = no credit.

1.  What is the discriminant of a quadratic function? How does the discriminant determine the number and type of solutions for a quadratic equation? (Answer in complete sentences)

2.  For 2x + bx + 2, what values of b give:

  1. Two imaginary solutions?
  2. Two real answers?
  3. One real solution?

3.  The following table shows the average number of hours per person per year spent on the internet between 1997 and 2001. Graph on a scatterplot and find a best fitting quadratic which represents this data.

1997 / 1998 / 1999 / 2000 / 2001
Time spent (hours) / 34 / 54 / 82 / 106 / 134

4.  Find the equation of the quadratic that passes through the following points:

(-1, 13), (1, 6), (3, 9)

Graph the following quadratics. At least three points should be labeled for each graph, including the vertex and y-intercept.

5.  y = 4x– 16x + 3

6.  y = (1/3)x+ 2x – 1

7.  y - x + 5x – 1

8.  y - (x – 3) (x – 1)

9.  y ½ (x + 2) (x – 4)

10.  y = (x + 2) (x + 3)

11.  y 2(x – 2)+ 1

12.  y = – (x + 1)+ 2

Factor the following completely:

13.  x – 9

14.  18x– 2

15.  x- 12x + 27

16.  x– 4x + 4

17.  2x– 4x – 6

18.  18x– 9x – 14

19.  20x– 54x + 36x

Simplify:

20. 

21.  (Bonus: How do the solutions to the resulting quadratic relate to the starting expression?)

22.  Find the absolute value of -4 + 5i

Solve by any method.

23.  3x+ 2x = 0

24.  4x + 4x – 6 = 0

25.  (x + 2)(x + 3) = 12

26.  (x – 2)– 12 = 0

27.  2x – x + 6 = 0

28.  When selling tickets for Carnegie’s theatre performance, ticket prices affect the number of people who buy tickets. If the prices are set at $12, then 300 people would attend over the course of the three performances. For every dollar cheaper the tickets are, 75 more people buy tickets to the show. What is the optimum price in order to maximize revenue? How much does Carnegie make at its maximum?

29.  Students are selling tickets to their international festival. On day 1, Carnegie students sold only 50 tickets. At the end of day 2, they had sold 200 tickets and at the end of day 4, they had sold 600 tickets. Write a quadratic that represents this data.

30.  The Biology club is constructing a turtle pen using 18 feet of donated fencing. They have two turtles who each need their own territory, so the pen must be a rectangle subdivided down the middle into two equal rectangles using part of the fencing. What is the maximum area of the turtle pen, and what dimensions should the pen have?


Quadratics Test Review Solutions

1.  The discriminant is b – 4ac. If it is < 0, then its quadratic equation has two imaginary solutions; if it is > 0, the equation has two real solutions; and if it is = 0, the equation has 1 real solution.

2.  -4 < b < 4, b > 4 or b < -4, b = 4 or -4

3.  Answers will vary

4. 

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12. 

13.  (x+3)(x-3)

14.  2(3x – 1)(3x + 1)

15.  (x – 3)(x + 3)(x– 3)

16.  (x – 2)

17.  2(x – 3)(x + 1)

18.  (3x + 2)(6x – 7)

19.  2x(2x – 3)(5x-6)

20. 

21.  x– 4x + 6

22. 

23.  x = 0,

24.  x =

25.  x = 1, -6

26.  x = 2()

27.  x =

28.  $8, $4800

29. 

30.  Max. area 13.5 sq. feet; dimensions 4.5 feet by 3 feet