Transcript Algebra 2 Final Review

Algebra 2 Final Review
Quadratics
1. Comparing the graph of y = -3x2 + 4x -1/2 to its parent function, it:
opens down and is wider than the parent function graph.
opens down and is narrower than the parent function graph.
opens up and is wider than the parent function graph.
opens up and is narrower than the parent function graph.
2. What is the equation of the axis of symmetry of y = 2x2 + 12x – 5?
A. X = -4
B. X = -3
c. X = 3
D. X = 4
3. What are the coordinates of the vertex of y = 2x2 + 12x – 5?
A) (-4 , -21)
B) (-3 , -23)
C) (3 , 49)
D) (4 , 75)
4. Which graph (to the right) has only one zero?
A
B
C
D
5. Which of the following is a step in solving y = 2x2 + 7x +6 by the Factoring
Method?
A) 2x + 3 = 0 or x + 2 = 0
B) 2x + 2 = 0 or x + 3 = 0
C) 2x + 1 = 0 or x + 6 = 0
D) 2x + 6 = 0 or x +1 = 0
6. The solution to (x + 9)2 = 25 is
A) -5 and 5
B) -4 and 4
C) -8 and 2
D) -4 and -14
7. What value goes in the blank to complete the square: x2 - 12x + ___?
A) -144
B) -36
C) 36
D) 144
8. What is the discriminant of 2x2 + 6x + 4 = 0?
A) 2
B) 4
C) 32
D) 68
9. How many real zeros does an equation have if the discriminant is 7?
A) 0
B) 1
C) 2
D) Not enough information
10. Solve 3x2 - 5x + 1 =0
A)
5± 13
6
B)
−5± −13
6
C)
−5± 13
6
D)
5± −13
6
11. Simplify
−4± 4
2
A) -6 and -2
B) -3 and -1
C) -4 and 0
D) -1 and 0
12. Given the height of a rocket as h = -16t2 + 160t + 384, the class was asked
when the rocket hits the ground. Kim solved to find the zeros t = -2 and t = 6.
Assuming the calculations were correct, what should the answer to teacher’s
question be?
A) Both -2 and 6 since the calculations were correct
B) 6 only since it has to be a positive
C) -2 since the sign needs to be changed
D) Neither, since the rocket will not hit the ground
13. Solve 2x2 + 7x + 6 = 0
A) -2 and -1.5
B) 2 and -1.5
C) -2
D) 2
14. Which correctly shows the quadratic in vertex form? 𝑦 = −2𝑥 2 + 12𝑥 − 8
A) 𝑦 = −2 𝑥 + 6 2 − 44
B) 𝑦 = −2 𝑥 − 3 2 − 26
C) 𝑦 = −2 𝑥 − 3 2 + 10
D) 𝑦 = −2 𝑥 + 3 2 − 26
15. Where is the vertex of 𝑦 = 𝑥 2 − 6𝑥 + 21
A) (3,12)
B) (-3,18)
C) (-3,12)
D) (3,-18)
16. What value goes in the blank to complete the perfect square
trinomial: x2 + __x + 16?
17. A square has its length increased by 6 feet and its width decreased by 4 feet; the
resulting area is 96 square feet. What was the area of the original square?
18. Solve (2x+5)(x+4)=0
19. Solve the following quadratics using the method of your choice:
A) 𝑝2 + 𝑝 − 72 = 0
B) 4𝑚2 − 100 = 0
C) 𝑔2 + 4𝑔 = 12
D) −2𝑥 2 + 8𝑥 − 5 = 0
20. A rectangle has a length 10 more than its width. If the width is increased by 8 and the
length by 4, the resulting rectangle has an area of 135 square units.
A) What is the length of the original rectangle?
B) What is the perimeter of the expanded rectangle?
21. Two boats leave the same dock at the same time. One boat travels South, and the other
travels East. After 3 hours, the boat traveling South had traveled 13 more miles than the
other. At this time, the boats were 77 miles apart. How far did each boat travel?