Download Algebra 2 Name QUARTERLY 2 REVIEW (part 1

Algebra 2
Name ________________________
QUARTERLY 2 REVIEW (part 1)
Block_________________________
Solve. Write answers in simplest form.
1. -2 = -3x2 + 8x
2. 4x2 + 7x -11 = 0
3. Solve 3x2 + 81 = 0 .
4. Multiple Choice: Which quadratic equation has the roots -½ and 4?
a) 2x2 – 4x + 4 = 0
c) 2x2 +1/2x - 4 = 0
b) 2x2 + 7x – 4 = 0
d) 2x2 – 7x – 4 = 0
5. Write the equation of a quadratic whose x intercepts are -8 and 13.
6. Find the value of c to make a perfect square trinomials. Then rewrite as a perfect square.
x2 - 12x + c
For 7-9, simplify completely. Show all work.
8. 2(6 + 8i)  i(4 – 5i)
7. i247
10. Rationalize
3 i
4  2i
9. (3+ 7i)2
11. Evaluate |3 – 2i|

12. a. Describe the transformation of the parabola h(x) = -3(x + 2)2 - 6 as compared to g(x) = x2.
b. The vertex of the parabola is:
13a. Graph using any method.
f(x) = -2x2 – 7x + 4
1
b. On the same axes, graph f(x) =  x  4
2

c. At what point(s) do the graphs of the equations intersect
14. A rocket is launched at 19.6 meters per second (m/s) from a 48.8-meter tall platform. The equation
for the object's height s at time t seconds after launch is s(t) = –4.9t2 + 19.6t + 48.8, where s is in meters.
Only an algebraic solution will be accepted. Show all work clearly.
a) What will the height of the rocket be after 3.5 seconds?
b) At what time will the rocket reach maximum height?
c) What is the maximum height of the rocket?
d) To the nearest tenth of a second, when will the rocket be 55 meters off the ground?
e) To the nearest tenth of a second, when does the object strike the ground?
Algebra 2
Name ________________________
QUARTERLY 2 REVIEW (part 2)
Block_________________________
1) Determine the roots of the equation: 4x2 + 8x – 12 = 0.
A.
C.
x = {-1, 3}
x = {2, 6}
B.
D.
x = {-3, 1}
x = {-2, -6}
2) Determine the number of roots: x2 – 4x + 4
A. 2 real, rational roots
C. 2 real, irrational roots
B. 1 real, rational root
D. 2 imaginary roots
3) Write the equation of a quadratic whose x intercepts are –
A.
C.
x2 – 20x – 5
4x2 – 47x – 12
B.
D.
4x2 + 47x – 12
x2 + 20x + 5

B.
D.
i
-i
B.
D.
10 – 3i
-14 – 3i
B.
D.
24 – 10i
-24 + 10i
4) Simplify i215.
A.
C.
1
-1
5) Simplify 3(4 + 9i)  2i(6 + i).
A.
C.
14 + 15i
12 – 3i – 2i2
6) Simplify (1+ 5i)2.
A.
C.
1+ 25i2
-24
1
and 12.
4
7) Describe the transformation of the parabola h(x) = 7(x + 4)2 as compared to g(x) = x2.
A. Dilation of 7 and Translation left 4
C. Dilation of 7 and Translation right 4
B. Reflection and Translation left 4
D. Reflection and Translation right 4
8). The solutions of a quadratic equation are {4, 8}. How many times will the graph of the quadratic
equation intersect the x axis?
A. 0
C. 2
B. 1
D. 3
9) Find the values of a and b that make the equation true. (5 + a) + (2b – 1)i = -12 + 9i
A.
C.
a = -7 b = 4
a = 7 b = -4
B.
D.
a = - 17
a = 17
B.
D.
√59
√61
b=5
b = -5
10) Evaluate 6  5i
A.
C.
59
3√5
11) Which represents the axis of symmetry for g(x) = -2x2 – 5x + 4?
A.
C.
x = 5/4
x = -5/4
B.
D.
12) Simplify completely √𝟔𝟎
A.
C.
13)
7.7
2√𝟑𝟎
Evaluate ⟦𝑥 − 6⟧ − 1 if x = 8.8
A.
0
B.
-2
C.
1
D.
3
B.
D.
2√𝟏𝟓
4√𝟏𝟓
y = 5/4
y = -5/4
14) If x(x-3)(3x+5) = 0, the x is equal to
A.
C.
0, -3, -5/3
3, -3/5
B.
D.
0, 3, -5/3
-3, 3/5
For 15 – 20, Match each equation with the corresponding graph. Write the equation on the line.
a) y = 4x2 + 2x – 3
b) y = -2x2 + x + 1
c) y = 2x2 – 2x + 1
d) y = -½x + 4
e) y = |x – 2| - 1
f) y = 2|x+2| - 1
15) ___________________
18) ___________________
16) ___________________
17) ___________________
19) ___________________
20) ___________________
For 21 – 27, match the terms with the definitions.
21) _____ Discriminant
a) A transformation in which the figure is either enlarged or reduced
22) _____Quadratic Function
b) An example is -3 + 4i
23) _____Parabola
c) The graph of a quadratic function
24) _____Dilation
d) The expressions a + bi and a – bi
25) _____Conjugates
e) ax2 + bx + c where a ≠ 0
26) _____Pure Imaginary
27) _____Complex
f) The expression b2 – 4ac
g) An example is 2/5i