Download test three

Intermediate Algebra test three
Thursday, December 6, 2007
please show relevant work to get full credit for each problem
1. Simplify each of the following radical expressions:
√
(a)
2. Rewrite
√
3
(b)
√
−16
(c)
√
3
−8x12
x2 using a fractional exponent. 3. Rewrite x7/2 using a radical.
√
4. Simplify:
20
√
75x3 − x 12x
5. Simplify x4/3 x−1/3
6. Rationalize the denominator & simplify:
−2
√
5 2
√
6
7. Solve the equation x2 + 8x + 14 = 0 using the method of completing the square:
8. Simplify the product of complex numbers
(1 + 2i)(3 − i) where i =
9. Rationalize the denominator & simplify:
√
−1
√
√
2+ 3
√
√
5+ 6
10–14. Solve each of the following equations:
10. (1 + x)2 = 3
√
12. x + 4 = 3x + 22
14. x4 − 5x2 − 36 = 0
11.
√
x = −4
13. 4x2 − 2x − 1 = 0
page two
15. The quadratic equation
y = −(x − 3)2 + 4
graphs as a parabola. Specify the x and y coordinates of the vertex. (It is not necessary to
sketch the graph).
16. Graph the parabola, showing the vertex and x & y intercepts
y = 2x2 + 8x + 6