Download MATH 64/GRACEY

MATH 64/GRACEY
11.1-11.2
Name___________________________________
Solve the equation by the square root property. If possible, simplify radicals or rationalize denominators. Express
imaginary solutions in the form a + bi.
1) 6x2 = 96
2) 144x2 = 25
3) 14x2 - 5 = 0
4) (x - 3)2 = 16
5) (x + 2)2 = 12
1
6) x -
5 2 121
=
2
4
7) (x - 7)2 = -36
Solve the problem.
8) If f(x) = (x - 2)2 , find all values of x for which f(x) = 49.
Complete the square for the binomial. Then factor the resulting perfect square trinomial.
9) x2 + 6x
10) x2 - 18x
11) x2 +
1
x
4
2
Solve the quadratic equation by completing the square.
12) x2 - 10x + 21 = 0
13) x2 + 5x - 5 = 0
14) x2 + 6x + 18 = 0
3
15) 16x2 - 7x + 1 = 0
Solve.
16) The formula F = 0.02x2 + 22 models the percentage of female tenured faculty, F, at State University x years after
1980. According to the formula, in what year will the percentage of female tenured faculty reach 35.52?
17) The function s(t) = 16t2 models the distance, s(t), in feet, that an object falls in t seconds. Find the number of
seconds a sky diver is in free fall after jumping from a plane if she falls 960 feet before opening a parachute.
Express your answer in simplified radical form.
4
18) A square flower bed is to be enlarged by adding 3 meters on each side. If the larger square has an area of 169
square meters, what is the length of a side of the original square?
Solve the formula for the specified variable. Assume all variables represent nonnegative numbers. If possible, simplify
radicals and rationalize denominators.
19) V = πr2 h for r
Find the distance between the pair of points. Give an exact answer.
20) (-4, 4) and (-9, -8)
21) (2, 5) and (-3, -2)
22) (3 2, -4) and (7 2, -2)
5
Find the midpoint of the line segment with the given end points.
23) (2, -5) and (4, 5)
24) (-9, -9) and (7, 0)
25) (-6 7, 5 6) and (-3 7, 8 6)
Use the quadratic formula to solve the equation.
26) x2 - 7x + 6 = 0
6
27) x2 + 7x + 7 = 0
28) -8x2 + 7x - 5 = 0
29) 2x2 = -8x - 1
7
30) x(x - 8) = 4
Use the discriminant to determine the number and type of solutions for the given equation.
31) x2 - 5x + 4 = 0
32) x2 + 5x + 3 = 0
Solve the equation by the method of your choice. Simplify solutions, if possible.
33) x2 + 18x = -53
8
34) (2x - 3)2 = 121
35)
1
1 1
+ =
x + 11 x 8
Write a quadratic equation in standard form with the given solution set.
36) {9, 8}
9
37) {-6i, 6i}
Solve the problem.
38) The length of a rectangular storage room is 5 feet longer than its width. If the area of the room is 150 square
feet, find its dimensions.
39) The hypotenuse of an isosceles right triangle is 3 feet longer than either of its legs. Find the exact length of each
side.
10
Answer Key
Testname: M64_11.1-11.2_FA13
1) { ± 4}
5
2) ±
12
3) ±
70
14
{7, -1}
{ -2 + 2 3, -2 - 2 3 }
{8, -3}
7 ± 6i
-5, 9
9) x2 + 6x + 9 = (x + 3)2
10) x2 - 18x + 81 = (x - 9)2
1
1
1 2
11) x2 + x +
= x+
4
64
8
4)
5)
6)
7)
8)
12) {7, 3}
-5 ± 3 5
13)
2
14) -3 ± 3i
7 ± i 15
15)
32
16) 2006
17) 2 15 seconds
18) 7 meters
πVh
19) r =
πh
20) 13 units
21) 74 units
22) 6 units
23) 3, 0
9
24) - 1, 2
25)
-9 7 13 6
,
2
2
26) {6, 1}
-7 ± 21
27)
2
28)
-7 ± i 111
-16
29)
-4 ± 14
2
30)
31)
32)
33)
34)
{4 ± 2 5}
Two rational solutions
Two irrational solutions
{-9 ± 2 7}
{7, -4}
11
Answer Key
Testname: M64_11.1-11.2_FA13
35)
5±
377
2
36) x2 - 17x + 72 = 0
37) x2 + 36 = 0
38) 10 feet by 15 feet
39) 3 + 3 2 feet
3 + 3 2 feet
6 + 3 2 feet
12