Question : Fill in each blank with one of the words or phrases listed below. Some choices : 2163447
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Fill in each blank with one of the words or phrases listed below. Some choices may be used more than once and some may not be used at all.
1) If x2 = a, then x = √(a) or x = -√(a). This property is called the _____ property.
A) square root
B) quadratic
C) vertex
D) completing the square
2) The graph of y = x2 is called a(n) _____.
A) parabola
B) vertex
C) quadratic
D) square root
3) The formula (-b/2a) where y = ax2 + bx + c is called the _____ formula.
A) completing the square
B) vertex
C) square root
D) quadratic
4) The process of solving a quadratic equation by writing it in the form (x + a)2 = c is called _____.
A) vertex
B) square root
C) quadratic
D) completing the square
5) The formula x = (-b ± √(b2 - 4ac)/2a) is called the _____ formula.
A) vertex
B) square root
C) completing the square
D) quadratic
6) The lowest point on a parabola that opens upward is called the _____.
A) vertex
B) quadratic
C) one
D) zero
7) The zero-factor property states that if the product of two numbers is zero, then at least one of the two numbers is _____.
A) one
B) quadratic
C) parabola
D) zero
Solve by factoring.
8) x2- 49 = 0
A) x = ±8
B) x = 7
C) x = 24.5
D) x = ±7
9) 3x2 - 5x = 8
A) x = (3/8), 1
B) x = (3/8), 0
C) x = (8/3), -1
D) x = (3/8), -1
Solve using the square root property.
10) 5k2 = 245
A) k = ±7
B) k = ± (49/2)
C) k = ± (7√(5)/5)
D) k = 2401
11) (2m - 1)2 = 27
A) m = (1 ± 3√(3)/2)
B) m = (3√(3) ± 1/2)
C) m = (1 ± 9√(3)/2)
D) m = (1 + 3√(3)/2)
Solve by completing the square.
12) a2 + 2a - 48 = 0
A) a = ±√(-48)
B) a = -40, -8
C) a = 6, -8
D) a = -6, 8
13) 2m2 + 12m + 1 = 0
A) m = (-6 ± √(38)/2)
B) m = (-6 ± √(34)/4)
C) m = (-6 ± √(34)/2)
D) m = (-12 ± √(34)/2)
Solve using the quadratic formula.
14) x2 + 4x + 3 = 0
A) x = 1, -1
B) x = 1, 3
C) x = 6, -3
D) x = -1, -3
15) p2 - (5/4)p + (3/4) = 0
A) p = (5 ± √(1)/4)
B) no real solutions
C) p = (-5 ± √(-23)/8)
D) p = (5 ± √(1)/16)
Solve by the most appropriate method.
16) (2x - 1)(x + 4) = 35
A) x = -3, (13/2)
B) x = - (13/2), 3
C) x = -4, 3
D) x = -4, (1/2)
17) (2m - 1)2 = 9
A) m = 2, -4
B) m = 4, -2
C) m = 1, -2
D) m = 2, -1
18) 7k2 - 5k - 5 = 0
A) k = (5 ± √(165)/7)
B) k = (-5 ± √(165)/14)
C) k = (5 ± √(165)/14)
D) k = (5 ± √(95)/28)
19) x2 - 12x + 32 = 0
A) x = 8, 4
B) x = 32, 0
C) x = -8, -4
D) x = -8, 4
20) 2x2 - 7x - 9 = 0
A) x = (2/9), -1
B) x = (2/9), 1
C) x = (9/2), -1
D) x = (2/9), 0
21) 3m2 + 12m + 5 = 0
A) m = (-6 ± √(51)/3)
B) m = (-12 ± √(21)/3)
C) m = (-6 ± √(21)/6)
D) m = (-6 ± √(21)/3)
Solve the problem.
22) The height of a triangle is 4 times the length of the base. The area of the triangle is 162 square meters. Find the height and base of the triangle.
A) base: 9 m, height: 36 m
B) base: (9/2) m, height: 72 m
C) base: (9√(2)/2) m, height: 18√(2) m
D) base: 36 m, height: 72 m
Graph the quadratic equation. Identify the vertex and the intercepts.
23) y = -2x2
A) Vertex: (0, 0)
x-intercepts: none
y-intercepts: none
B) Vertex: (0, -2)
x-intercepts: none
y-intercepts: none
C) Vertex: (0, 0)
x-intercepts: none
y-intercepts: none
D) Vertex: (0, 0)
x-intercepts: none
y-intercepts: none
24) y = x2 - 9
A) Vertex: (0, -9)
x-intercepts: none
y-intercept: (0, -9)
B) Vertex: (0, 9)
x-intercepts: none
y-intercept: (0, 9)
C) Vertex: (0, -9)
x-intercepts: (-3, 0), (3, 0)
y-intercept: (0, -9)
D) Vertex: (-9, 0)
x-intercept: (-9, 0)
y-intercept: (0, 81)
25) y = x2 + 2x - 8
A) Vertex: (- 1, - 9)
x-intercepts: (4, 0), (2, 0)
y-intercept: (0, -8)
B) Vertex: (1, - 9)
x-intercepts: (-2, 0), (4, 0)
y-intercept: (0, 8)
C) Vertex: (- 1, - 9)
x-intercepts: (-4, 0), (2, 0)
y-intercept: (0, -8)
D) Vertex: (1, - 9)
x-intercepts: (-2, 0), (4, 0)
y-intercept: (0, -8)
26) y = 2x2 + 2x - 1
A) Vertex: (- (1/2), - (3/2))
x-intercepts: ((-1 - √(7)/2), 0), ((-1 + √(7)/2), 0)
y-intercept: (0, -1)
B) Vertex: ((1/2), - (3/2))
x-intercepts: ((1 - √(3)/2), 0), ((1 + √(3)/2), 0)
y-intercept: (0, -1)
C) Vertex: (- (1/2), - (3/2))
x-intercepts: ((-1 - √(3)/2), 0),((-1 + √(3)/2), 0)
y-intercept: (0, -1)
D) Vertex: ((1/2), - (3/2))
x-intercepts: ((1 - √(7)/2), 0), ((1 + √(7)/2), 0)
y-intercept: (0, -1)
Solve.
27) The number of diagonals d that a polygon with n sides has is given by the formula
d = (n2 - 3n/2) Find the number of sides of a polygon if it has 44 diagonals.
A) 12
B) 8
C) 11
D) 10
28) Neglecting air resistance, the distance h traveled by a free-falling object in time t is given by the formula h = 16t2. Use this formula to find the time of free fall for a parachutist who falls 3519 feet before opening her parachute. Round your answer to the nearest tenth of a second.
A) 14.8 sec
B) 3.7 sec
C) 110 sec
D) 237.3 sec
