1
1
Math 70 : Intermediate Algebra
Test 5: Quadratic Equations and Inequalities
Name: __________________________
You have to show your work.
No credit will be given if you do not show your work.
Circle your answers.
Number
1
2
3
4
5
6
7
8
9
10
11
Points Your score Comments
5
5
6
8
8
8
10
10
10
12
8
Total
90
Your test score = _____________________
Your course grade = __________________
1
Fall 2010
2
1. [5] Solve by taking square roots: 2( x  1) 2  24  0.
Answer: x  1  2i 3
2. [5] Write a quadratic equation (ax  bx  c  0) that has 2 2 and  2 2 as
solutions.
2
Answer:
x2  8  0
3. [6] Use completing the square method to solve: x 2  6 x  11  0.
Answer:
x  3  2 5
4. [8] Use the discriminant to determine whether the equation has one real number
solution, two real number solutions or two complex number solutions.(Justify
your answer.)
(a) 9 x 2  12 x  4  0.
(b) 2 x 2  x  5  0.
Answer: D= 0, double roots.
(One real solution.)
D= -39 < 0, Two complex roots
5. [8] Solve : x 4  3 x 2  4  0. Answer: x  1 ,  2i
2
1
6. [8] Solve: x 3  3 x 3  4  0 . Answer: x = 64 or -1
7. [10] Solve: x  1  3x  5.
Give the exact solution and an approximated solution to the nearest hundredth.
x
7  13
7  13
 5.30 or x 
 0.70
2
2
3
8. [10] A car travels 120 miles. A second card traveling 20 miles faster than the first
car, making the same trip in 2 hour less time. Find the speed of the first car.
Give the exact solution and an approximated solution to the nearest hundredth.
Distance
120
120
First car
Second car
120
120
2
x
x  20
Rate
x
x+20
Time
x  10  10 13 or x  10  10 13  0 (impossible)
The first car:  10  10 13 mph, approximately, 26.06 mph
9.
x
 1 . Use the method we discussed in class. Present your
2x  1
solution set in set builder form and graph your solution set. Answer: (–∞, ½) U
[1, ∞)
[10] Solve:
10. [12] y  x 2  x  2.
(a) Find the axis of symmetry:
x= 
1 1

2 1 2
(b) Find the vertex. (0.5, -2.25)
(c) Find the x-intercepts and the y-intercept.
x-intercept:
( 2, 0) ( –1, 0)
(d) Use all the information to sketch the graph. On your graph, mark all the
information you obtained in parts (a), (b) and (c).
11. [8] The height s, in feet, of a rock thrown upward at an initial speed of 64
ft/second from a cliff 50 ft above an ocean beach is given by the function
s(t )  16t 2  64t  50, where t is the time in seconds.
Find the amount time it will take the rock to attain the maximum height above the
beach and find the maximum height.
Time: 2 seconds. The maximum height is 114 ft.