Algebra 2 ~ Test Chapter 5
Directions: Show all work and reasoning to receive full credit.
Name:
Rewrite in standard form y  ax  bx  c and determine whether each function is linear or quadratic.
2
1.
y  x  2x  4
2. y  5 x x  5  5 x
2
Identify the vertex and axis of symmetry.
3.
5
4.
3
4
2
1
-3
-2
-1
3
1
2
3
4
2
Vertex:
5
-1
Vertex:
1
-2
Axis of symm:
-3
-4
-3
-2
-1
1
2
3
4
Axis of symm:
-1
-4
-2
-5
-3
5. Americans spend a considerable amount of money on personal technology every year. The table shows how much was spent each
year starting with 1970 (which we are considering year zero).
0
8.8
Year (0 = 1970)
Billions of Dollars
10
17.6
20
53.8
22
61.2
24
78.5
26
89.7
a. Use your calculator to find a quadratic regression for this data (round decimals to the nearest thousandth):
b. Use the model to estimate the billions of dollars spent on technology in year 16 (1986):
Graph the functions.
6. y  2 x  4 x  3
7. y   x  2 x  5
2
2
Up or down (answer only):
Vertex (work and answer):
Up or down (answer only):
Vertex (work and answer):
y – intercept (answer only):
y – intercept (answer only):
10
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
2
4
6
8 10
-10 -8 -6 -4 -2
2
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
4
6
8 10
Write each function in vertex form y  a( x  h)2  k . Sketch the graph of the function and label its vertex.
y = 2x2 + 8x
8.
y = –x2 + 4x – 1
9.
10
10
8
8
6
6
4
4
2
-10 -8 -6 -4 -2
2
2
4
6
8 10
-10 -8 -6 -4 -2
2
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
4
6
8 10
Simplify each expression.
10.
 50
Simplify each expression.
12. (3  i )  (7  6i )
11.
13. (4  9i )  (5  7i )
15. Find the additive inverse of the complex number.
 7  2i
 12
14. (3  4i )(5  2i )
16. Graph the complex number and find its absolute value.
8  10i
Imaginary
10
8
6
4
2
-10 -8 -6 -4 -2
2
-2
-4
-6
-8
-10
4
6
8 10
Real
SOLVE each quadratic equation by using the quadratic formula.
17.
x2  4 x  2  0
Solve by completing the square.
19. x2 + 4x – 21 = 0
18. 2 x  4 x  4  0
2
20.
3x2 + 18x + 36 = 0
Find the discriminant of each equation. SHOW ALL WORK! How many real OR imaginary solutions does each have?
21. x  4 x  3  0
2
22. 3 x  4 x  3  0
2
23. A ball has been thrown upward from ground level. Its height h, in feet, above the ground after t seconds is h  48t  16t .
2
(a) Find the amount of time that it will take for the ball to reach its maximum height.
(b) Find the maximum height of the ball.
Factor the expressions completely.
24.
x 2  3x  40
25.
x 2  8x  16
26.
9x 2  4
27.
6 x2  5x  4
28.
18x 2  24x  10
29.
5x 2  12x  32
Solve problems 30 and 31 by finding square roots.
30.
31. 2( x  8)  50  18
2
2x2 + 5 = 205
Solve problems 32 and 33 by factoring.
Solve problem 34 by graphing on your calculator.
5
32. 2x2 – 10x = 0
33.
2 x2  x 15  0
4
34. 2x2 + x – 3 = 0
Sketch your graph here:
3
2
1
-5 -4 -3 -2 -1
1
-1
-2
-3
-4
-5
2
3
4
5