Title: Chapter 10 Quadratic Equations and Functions
Course: quiz duplicate error

Q: Identify the vertex of the graph. Tell whether it is a minimum or maximum.
[Image]
- (0, –1); minimum
- (–1, 0); maximum
- (0, –1); maximum
- (–1, 0); minimum
A: (0, –1); maximum

Q: Which of the quadratic functions has the narrowest graph?
- [Image]
- [Image]
- [Image]
- [Image]
A: [Image]

Q: Which of the quadratic functions has the widest graph?
- [Image]
- [Image]
- [Image]
- [Image]
A: [Image]

Q: Order the group of quadratic functions from widest to narrowest graph.
[Image], [Image], [Image]
- [Image], [Image], [Image]
- [Image], [Image], [Image]
- [Image], [Image], [Image]
- [Image], [Image], [Image]
A: [Image], [Image], [Image]

Q: If [Image], then the graph of [Image] is ________ narrower than [Image].
- always
- sometimes
- never
A: always

Q: If an object is dropped from a height of 38 feet, the function [Image] gives the height of the object after t seconds. Graph the function.
- [Image]
- [Image]
- [Image]
- [Image]
A: [Image]

Q: A parabola ________ has an axis of symmetry.
- always
- sometimes
- never
A: always

Q: Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the function.
[Image]
- [Image]; vertex: [Image]
- [Image]; vertex: [Image]
- [Image]; vertex: [Image]
- [Image]; vertex: [Image]
A: [Image]; vertex: [Image]

Q: Graph [Image]. Label the axis of symmetry and vertex.
- [Image] Axis of symmetry: [Image] Vertex: [Image]
- [Image] Axis of symmetry: [Image] Vertex: [Image]
- [Image] Axis of symmetry: [Image] Vertex: [Image]
- [Image] Axis of symmetry: [Image] Vertex: [Image]
A: [Image] Axis of symmetry: [Image] Vertex: [Image]

Q: Suppose you have 54 feet of fencing to enclose a rectangular dog pen. The function [Image], where x = width, gives you the area of the dog pen in square feet. What width gives you the maximum area? What is the maximum area? Round to the nearest tenth as necessary.
- width = 27 ft; area = 182.3 ft^2
- width = 27 ft; area = 391.5 ft^2
- width = 13.5 ft; area = 546.8 ft^2
- width = 13.5 ft; area = 182.3 ft^2
A: width = 13.5 ft; area = 182.3 ft^2

Q: A ball is thrown into the air with an upward velocity of 36 ft/s. Its height h in feet after t seconds is given by the function [Image].
a. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary.
b. What is the ball’s maximum height?
- 1.13 s; 69.75 ft
- 1.13 s; 29.25 ft
- 1.13 s; 31.5 ft
- 2.25 s; 9 ft
A: 1.13 s; 29.25 ft

Q: Graph [Image].
- [Image]
- [Image]
- [Image]
- [Image]
A: [Image]

Q: Solve [Image] by graphing the related function.
- [Image] There are two solutions: 2 and –2.
- [Image] There are two solutions: [Image].
- [Image] There are two solutions: 2 and –2.
- [Image] There are no real number solutions.
A: [Image] There are two solutions: 2 and –2.

Q: The quadratic equation [Image], where a > 0, ________ has at least one real number solution.
- always
- sometimes
- never
A: never

Q: Solve the equation using square roots.

7 [Image] + 6 = 13
- no real number solutions
- 1
- [Image]
- [Image]
A: [Image]

Q: Solve the equation using square roots.

[Image]
- [Image]
- –4
- [Image]
- no real number solutions
A: no real number solutions

Q: Solve the equation using the zero-product property.

[Image]
- x = –1 or x = [Image]
- x = –1 or x = [Image]
- x = 1 or x = [Image]
- x = 1 or x = [Image]
A: x = –1 or x = [Image]

Q: Solve the equation using the zero-product property.

[Image]
- n = [Image] or n = [Image]
- n = 0 or n = [Image]
- n = 0 or n = [Image]
- n = [Image] or n = [Image]
A: n = 0 or n = [Image]

Q: A sports recreation company plans to manufacture a beach ball with a surface area of 7238 in.^2 Find the radius of the beach ball. Use the formula [Image], where A is the surface area and r is the radius of the sphere.
- 24 in.
- 48 in.
- 75 in.
- 576 in.
A: 24 in.

Q: Find the value of x. If necessary, round to the nearest tenth.
[Image]
- 7.3 in.
- 10.3 in.
- 12.4 in.
- 14.6 in.
A: 10.3 in.

Q: Solve the equation by factoring.

[Image]
- z = 3 or z = 9
- z = 3 or z = –9
- z = –3 or z = 9
- z = –3 or z = –9
A: z = –3 or z = 9

Q: Solve the equation by factoring.

[Image]
- z = [Image] or z = –2
- z = [Image] or z = 2
- z = 3 or z = –2
- z = 3 or z = 2
A: z = [Image] or z = –2

Q: Solve the equation by factoring.

[Image]
- c = 0 or c = –4
- c = 0 or c = [Image]
- c = 0 or c = 4
- c = 1 or c = – [Image]
A: c = 0 or c = 4

Q: Solve the equation by factoring.

[Image]
- [Image]
- [Image]
- [Image]
- [Image]
A: [Image]

Q: Solve the equation by factoring.

The expression [Image] ________ has the solution x = 0.
- always
- sometimes
- never
A: always

Q: Tasha is planning an expansion of a square flower garden in a city park. If each side of the original garden is increased by 7 m, the new total area of the garden will be 144 m^2. Find the length of each side of the original garden.
- 19 m
- 12 m
- 5 m
- [Image] m
A: 5 m

Q: The area of a playground is 336 yd^2. The width of the playground is 5 yd longer than its length. Find the length and width of the playground.
- length = 26 yd, width = 21 yd
- length = 21 yd, width = 26 yd
- length = 21 yd, width = 16 yd
- length = 16 yd, width = 21 yd
A: length = 16 yd, width = 21 yd

Q: Solve the cubic equation by factoring.
[Image]
- [Image]
- [Image]
- 0, [Image]
- [Image]
A: [Image]

Q: Find the value of n such that [Image] is a perfect square trinomial.
- [Image]
- [Image]
- 361
- [Image]
A: [Image]

Q: Solve the equation by completing the square. Round to the nearest hundredth if necessary.

[Image]
- 5, –1
- 11, –7
- 1.73, –1.73
- 1, 3
A: 5, –1

Q: Solve the equation by completing the square. Round to the nearest hundredth if necessary.

[Image]
- 4.66, 5.12
- 3.62, –6.62
- 3.55, –6.55
- 24.75, –27.75
A: 3.62, –6.62

Q: Solve the equation by completing the square. Round to the nearest hundredth if necessary.

[Image]
- 1.05, –4.05
- 1.66, 2.69
- 1.19, –4.19
- –8.75, 5.75
A: 1.19, –4.19

Q: Solve the equation by completing the square. Round to the nearest hundredth if necessary.

3 [Image]
- 2.65, 3
- –30, 36
- 4, –2
- 7.58, –1.58
A: 4, –2

Q: Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.

[Image]
- 18, 28
- –9, –14
- 9, 14
- –18, 28
A: 9, 14

Q: Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.

[Image]
- 1.82, –0.22
- 11.2, –9.6
- 3.64, –0.44
- 0.22, –1.82
A: 1.82, –0.22

Q: Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.

A rocket is launched from atop a 101-foot cliff with an initial velocity of 116 ft/s.
a. Substitute the values into the vertical motion formula [Image]. Let h = 0.
b. Use the quadratic formula find out how long the rocket will take to hit the ground after it is launched. Round to the nearest tenth of a second.
- [Image]; 0.8 s
- [Image]; 8 s
- [Image]; 0.8 s
- [Image]; 8 s
A: [Image]; 8 s

Q: The solutions given by the quadratic formula are ________ integers.
- sometimes
- always
- never
A: sometimes

Q: Use any method to solve the equation. If necessary, round to the nearest hundredth.

[Image]
- 3.45, –1.16
- –3.45, 1.16
- 2.3, –2.3
- 6.89, –2.32
A: 3.45, –1.16

Q: Use any method to solve the equation. If necessary, round to the nearest hundredth.

[Image]
- 0.42, –2.71
- 2.71, –0.42
- 35.43, –33.14
- 5.42, –2.95
A: 2.71, –0.42

Q: Use any method to solve the equation. If necessary, round to the nearest hundredth.

[Image]
- 2.83, –2.83
- 1.17, –1.17
- 3.32, –3.32
- 0.85, –0.85
A: 0.85, –0.85

Q: Use any method to solve the equation. If necessary, round to the nearest hundredth.

[Image]
- 2.45, –2.45
- 1.15, –1.15
- 0.87, –0.87
- 2.83, –2.83
A: 0.87, –0.87

Q: For which discriminant is the graph possible?
[Image]
- [Image]
- [Image]
- [Image]
A: [Image]

Q: Find the number of real number solutions for the equation.

[Image]
- 0
- 1
- 2
A: 2

Q: Find the number of real number solutions for the equation.

[Image]
- 2
- 0
- 1
A: 0

Q: Graph the set of points. Which model is most appropriate for the set?
(–6, –1), (–3, 2), (–1, 4), (2, 7)
- [Image] linear
- [Image] quadratic
- [Image] exponential
- [Image] linear
A: [Image] linear

Q: Graph the set of points. Which model is most appropriate for the set?
(–2, 10), (–1,1), (1, 1), (2, 10)
- [Image] quadratic
- [Image] quadratic
- [Image] linear
- [Image] exponential
A: [Image] quadratic

Q: Which kind of function best models the data in the table? Graph the data and write an equation to model the data.

x | y
0 | –1
1 | –2
2 | –3
3 | –4
4 | –5
- [Image] exponential; y = 3^x – 1
- [Image] quadratic; y = x^2 – 1
- [Image] linear; y = –x – 1
- [Image] linear; y = x – 1
A: [Image] linear; y = –x – 1

Q: The table shows the estimated number of deer living in a forest over a five-year period. Are the data best represented by a linear, exponential, or quadratic model? Write an equation to model the data.

Year | Estimated Population
0 | 91
1 | 70
2 | 54
3 | 42
4 | 32
- exponential; [Image]
- linear; [Image]
- quadratic; [Image]
- quadratic; [Image]
A: exponential; [Image]

Q: In an exponential model, the y values ____ decrease as the x values increase.
- always
- sometimes
- never
A: sometimes

Q: The equation [Image] ____ has at least one real number solution when n > 0.
- always
- sometimes
- never
A: sometimes

Make a table of values and graph the quadratic function [Image].

x | [Image] | (x, y)

[Image]

An architect is designing an archway. The shape of the arch is described by the three inequalities given. Make a graph of the arch.

[Image]; [Image]; [Image]
[Image]

Solve [Image] by graphing the related function.
[Image]

a. Write an expression for the total area of the model below.
[Image]
b. The total area is 110 m^2. Write an equation to find x.
c. Solve the equation by completing the square.

The formula [Image] models the height of a model rocket, where h is the height in meters, t is the time in seconds and v is the initial vertical velocity in meters per second. If the model rocket is fired at an initial vertical velocity of 80 meters per second, will the rocket ever reach a height of 88 meters? Justify your answer.

Graph the data in the table below. Which kind of function best models the data? Write an equation to model the data.

x | y
0 | 30
1 | 6
2 | 1.2
3 | 0.24
4 | 0.048

[Image]

Graph the data in the table below. Which kind of function best models the data? Write an equation to model the data.

x | y
0 | –3
1 | –2
2 | –3
3 | –6
4 | –11

[Image]

For the equation [Image], find all the values of j such that the equation has two real number solutions. Show your work.

Graph the quadratic functions [Image] and [Image]. Compare the shape and position of the graphs.

The perimeter of a rectangular concrete slab is 114 feet and its area is 702 square feet. Find the dimensions of the rectangle.
a. Using l for the length of the rectangle, write an expression for the width of the rectangle in terms of l. (Hint: Solve the formula [Image] for w.) Show your work.
b. Write a quadratic equation using l, the expression you found in part (a), and the area of the slab.
c. Solve the quadratic equation. Use the two solutions to find the dimensions of the rectangle.

a. Which kind of function best models the data?
b. Write an equation to model the data.
c. If the pattern shown in the table continues, what is the value of y for x = 6? Round to the nearest hundredth if necessary.

x | y
0 | 30
1 | 15
2 | 7.5
3 | 3.75
4 | 1.875

Which method(s) would you choose to solve the equation? Justify your reasoning.

[Image]