AnswersASC Algebra I B MA272Solving Quadratic Equations: Quadratic Formula

Solving Quadratic Equations: Quadratic Formula — Cumulative exam Answers

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1
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Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = 9x2 – 36x?

A
The graph of f(x) = x2 is widened.
B
The graph of f(x) = x2 is shifted right 4 units.
C
The graph of f(x) = x2 is shifted down 36 units.
D
The graph of f(x) = x2 is reflected over the x-axis.
2
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three

T
The data point for x = 1 is above the line of best fit.
T
The residual value for x = 3 should be a positive number because the data point is above the line of best fit.
F
Fiona made a subtraction error when she computed the residual value for x = 4.
T
The residual value for x = 2 should be a positive number because the given point is above the line of best fit.
T
The residual value for x = 3 is negative because the given point is below the line of best fit.
3

Drew creates a table of ordered pairs representing the width and area of a dog pen.

Question illustration
D
Drew has 36 feet of fencing and wants to represent the possible areas of the dog pen for possible widths.
D
Drew has a maximum of 81 feet of fencing to use around the pen, and the length must be twice the width.
D
Drew is building a rectangular dog pen with a length that is up to 4 feet more than the width and has a perimeter of at least 77 feet.
D
Drew wants to build a dog pen that is between 7 feet and 11 feet in width and uses, at most, 18 feet of fencing.
4

Over which interval does the exponential show a more rapid rate of change?

Question illustration
A
mc025-2.jpg
Option A
B
mc025-3.jpg
Option B
C
mc025-4.jpg
Option C
D
mc025-5.jpg
Option D
5

The graph shows the exponential regression model for data representing a rabbit population after x years.

Question illustration
T
The graph of the regression model is limited to whole-number values for x.
T
The graph of the regression model is limited to whole-number values for y.
T
The graph of the regression model cannot be used to approximate the population size for year 1.
T
The graph of the regression model can be used to predict the population size for any number of years in the future.
6

Which of the following best describes how the y values are changing over each interval?xy122438416532

A
They are increasing by 2 each time.
B
They are increasing by 4 each time.
C
They are being multiplied by 2 each time.
D
They are being multiplied by 4 each time.
7

Heather is writing a quadratic function that represents a parabola that touches but does not cross the x-axis at x = –6. Which function could Heather be writing?

f
f(x) = x2 + 36x + 12
f
f(x) = x2 – 36x – 12
f
f(x) = –x2 + 12x + 36
f
f(x) = –x2 – 12x – 36
8

An architect designs a diagonal path across a rectangular patio. The path is 29 meters long. The width of the patio is x meters, and the length of the path is 5 meters more than the width.

Question illustration
A
0.5(x)(x + 5) = 29
B
0.5(x)(x + 5) = 841
C
x2 + (x + 5)2 = 29
D
x2 + (x + 5)2 = 841
9

Consider the quadratic function y = (x – 2)2 + 5. Which statements are true about the function and its graph? Select two options.The vertex of the function is (–2, 5).There are no real roots for the function.The graph of the function opens down.The graph contains the point (2, 5).The graph intersects the x-axis at one unique point.

Question illustration
A
The vertex of the function is (–2, 5).
B
There are no real roots for the function.
C
The graph of the function opens down.
D
The graph contains the point (2, 5).
E
The graph intersects the x-axis at one unique point.
10

Consider the quadratic function f(x) = x2 – 8x – 4. What is the value of the leading coefficient?

A
–8
B
–4
C
0
D
1
11

The table shows the height of a candle as it is continuously burned.

Question illustration
A
The candle starts at a height of 25 centimeters and burns at a rate of 0.625 centimeters per hour.
B
The candle starts at a height of 25 centimeters and burns at a rate of 2.5 centimeters per hour.
C
The candle starts at a height of 22.5 centimeters and burns at a rate of 0.625 centimeters per hour.
D
The candle starts at a height of 22.5 centimeters and burns at a rate of 2.5 centimeters per hour.
12

Over which interval are the exponential and linear function approximately the same?

Question illustration
A
from 0.25 to 0.5
B
from 0.5 to 0.75
C
from 0.75 to 1.0
D
from 1.25 to 1.5
13

Solve x2 – 8x = 20 by completing the square. Which is the solution set of the equation?

A
{–22, 14}
B
{–14, 22}
C
{–10, 2}
D
{–2, 10}
14

Sergey is solving 5x2 + 20x – 7 = 0. Which steps could he use to solve the quadratic equation by completing the square? Select three options.5(x2 + 4x + 4) = –7 + 20x + 2 = 5(x2 + 4x) = 75(x2 + 4x + 4) = 7 + 205(x2 + 4x) = –7

Question illustration
A
5(x2 + 4x + 4) = –7 + 20
B
x + 2 =
C
5(x2 + 4x) = 7
D
5(x2 + 4x + 4) = 7 + 20
E
5(x2 + 4x) = –7
15

Between which two ordered pairs does the graph of f(x) = x2 + x – 9 cross the negative x-axis?Quadratic formula: x =

Question illustration
A
(–6, 0) and (–5, 0)
B
(–4, 0) and (–3, 0)
C
(–3, 0) and (–2, 0)
D
(–2, 0) and (–1, 0)
16

The data in the table represents the predicted price of a gallon of milk, y, for number of years, x.

Question illustration
y
y = ax + b
y
y = ax2 + b
y
y = abx
y
y = a + bx
17

A rectangle’s length is 5 inches more than twice its width. Its area is 50 square inches. Which equation can be used to find its width, w?

A
2w(2w + 5) = 50
B
2w(w + 5) = 50
C
w(2w + 5) = 50
D
w(w + 5) = 50
18

The table shows the results of a survey of 400 random people on whether they like liquid soap, bar soap, or both. Which is the marginal relative frequency for the people who do not like bar soap?

Question illustration
A
StartFraction 100 Over 400 EndFraction
Option A
B
StartFraction 120 Over 400 EndFraction
Option B
C
StartFraction 280 Over 400 EndFraction
Option C
D
StartFraction 300 Over 400 EndFraction
Option D
19

The times of all 15 year olds who run a certain race are approximately normally distributed with a given mean = 18 sec and standard deviation = 1.2 sec. What percentage of the runners have times less than 14.4 sec?

Question illustration
A
0.15%
B
0.30%
C
0.60%
D
2.50%
20

two

T
The equation for the line of best fit is not a good approximation for the data because the points have a curved pattern.
T
The equation for the line of best fit is a good approximation for the data because the points are random, having no pattern.
T
The residual plot has a linear pattern.
T
The points of the residual plot are spread evenly above and below the x-axis.
T
The residual plot has the pattern of a curve.

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