Home
Subjects
Textbook solutions
Create
Study sets, textbooks, questions
Log in
Sign up
Upgrade to remove ads
Only $35.99/year
Math
Algebra
Quadratic Functions Unit Test
STUDY
Flashcards
Learn
Write
Spell
Test
PLAY
Match
Gravity
Terms in this set (76)
f(x)=a(x-h)^2+k
Vertex of a quadratic function (formula)
What is the axis of symmetry and vertex for the function f(x) = 3(x - 2)2 + 4?
x = 2
Vertex: (2, 4)
Which best describes the transformation from the graph of f(x) = x2 to the graph of
f(x) = (x - 3)2 - 1?
left 3 units, down 1 unit
left 3 units, up 1 unit
right 3 units, down 1 unit
right 3 units, up 1 unit
right 3 units, down 1 unit
The parent function of the function g(x) = (x - h)2 + k is f(x) = x2. The vertex of the function g(x) is located at (9, -8). What are the values of h and k?
g(x) = (x - )^2 +
9
-8
What is the equation of the translated function?
f(x) = (x - 1)2 - 5
f(x) = (x + 1)2 + 5
f(x) = (x - 5)2 - 1
f(x) = (x + 5)2 + 1
f(x) = (x + 1)2 + 5
Consider the graph of the function f(x) = 2(x + 3)2 + 2. Over which interval is the graph decreasing?
(-∞, -3)
(-∞, 2)
(-3, ∞)
(2, ∞)
(-∞, -3)
Which are characteristics of the graph of the function f(x) = (x + 1)2 + 2? Check all that apply.
The domain is all real numbers.
The range is all real numbers greater than or equal to 1.
The y-intercept is 3.
The graph of the function is 1 unit up and 2 units to the left from the graph of y = x2.
The graph has two x-intercepts.
The domain is all real numbers.
The y-intercept is 3.
Justine graphs the function f(x) = (x - 7)2 - 1. On the same grid, she graphs the function
g(x) = (x + 6)2 - 3. Which transformation will map f(x) on to g(x)?
left 13 units, down 2 units
right 13 units, down 2 units
left 13 units, up 2 units
right 13 units, up 2 units
left 13 units, down 2 units
The graph of which function is decreasing over the interval (-4, ∞)?
f(x) = (x + 4)2 + 4
f(x) = -(x + 4)2 + 4
f(x) = (x - 4)2 - 4
f(x) = -(x - 4)2 - 4
f(x) = (x - 4)2 - 4 - INCORRECT
What is the equation of the translated function, g(x), if
f(x) = x2?
g(x) = (x + 5)2 + 2
g(x) = (x + 2)2 + 5
g(x) = (x - 2)2 + 5
g(x) = (x - 5)2 + 2
g(x) = (x - 5)2 + 2
Over what interval is the graph of f(x) = -(x + 8)2 - 1 decreasing?
(-8, ∞)
Which best describes the transformation that occurs from the graph of f(x) = x2 to g(x) = (x - 2)2 + 3?
right 2, up 3
Which function has a range of {y|y ≤ 5}?
f(x) = -(x - 4)2 + 5
What value represents the vertical translation from the graph of the parent function f(x) = x2 to the graph of the function
g(x) = (x + 5)2 + 3?
3
The graph of f(x) = x2 is translated to form
g(x) = (x - 2)2 - 3.
Which graph represents g(x)?
A
Sanjay begins to correctly graph the function f(x) = (x + 1)2 - 3. Based on the axis of symmetry and the vertex, which graph could be Sanjay's?
C
Which function could be represented by the graph on the coordinate plane?
f(x) = (x - 8)2 + 6
f(x) = (x + 8)2 + 6
f(x) = (x + 8)2 - 6
f(x) = (x - 8)2 - 6
f(x) = (x - 8)2 - 6
What is the y-intercept of the quadratic function
f(x) = (x - 8)(x + 3)?
(8,0)
(0,3)
(0,-24)
(-5,0)
(0,-24)
What is the midpoint of the x-intercepts of
f(x) = (x - 2)(x - 4)?
(-3,0)
(-1,0)
(1,0)
(3,0)
(3,0)
Which function has two x-intercepts, one at (0, 0) and one at (4, 0)?
f(x) = x(x − 4)
f(x) = x(x + 4)
f(x) = (x − 4)(x − 4)
f(x) = (x + 4)(x + 4)
f(x) = x(x − 4)
Which point is an x-intercept of the quadratic function
f(x) = (x + 6)(x - 3)?
(0,6)
(0,-6)
(6,0)
(-6,0)
(-6,0)
What is the axis of symmetry of the function f(x) = -(x + 9)(x - 21)?
The axis of symmetry is x =
6
The graph of the function f(x) = (x - 4)(x + 1) is shown below.
Which statement about the function is true?
The function is increasing for all real values of x where
x < 0.
The function is increasing for all real values of x where
x < -1 and where x > 4.
The function is decreasing for all real values of x where
-1 < x < 4.
The function is decreasing for all real values of x where
x < 1.5.
The function is decreasing for all real values of x where
x < 1.5.
Which is the graph of f(x) = -(x + 3)(x + 1)?
B
The graph of the function f(x) = -(x + 6)(x + 2) is shown below.
Which statement about the function is true?
The function is increasing for all real values of x where
x < -4.
The function is increasing for all real values of x where
-6 < x < -2.
The function is decreasing for all real values of x where
x < -6 and where x > -2.
The function is decreasing for all real values of x where
x < -4.
The function is increasing for all real values of x where
x < -4.
The axis of symmetry for the graph of the function is f(x) = x2 + bx + 10 is x = 6. What is the value of b?
-3
The axis of symmetry for the function f(x) = −x2 − 10x + 16 is x = −5. What are the coordinates of the vertex of the graph?
(−5, 41)
(−5, 56)
(−5, 76)
(−5, 91)
(−5, 41)
The axis of symmetry for a function in the form f(x) = x2 + 4x − 5 is x = −2. What are the coordinates of the vertex of the graph?
(−9, −2)
(−17, −2)
(−2, −17)
(−2, −9)
(−2, −9)
The graph of which function has a y-intercept of 3?
A
Which is the graph of f(x) = x2 - 2x + 3?
NOT C, C IS INCORRECT
The graph of which function has an axis of symmetry at x = 3?
d
The axis of symmetry for the graph of the function f(x) = 3x2 + bx + 4 is x = . What is the value of b?
-9
Tempestt graphs a function that has a maximum located at (-4, 2). Which could be her graph?
C
What are the x-intercepts of the graph of the function f(x) = x2 + 4x - 12?
(-6, 0), (2,0)
(-2, -16), (0, -12)
(-6, 0), (-2, -16), (2, 0)
(0, -12), (-6, 0), (2, 0)
(-6, 0), (2,0)
liana started to evaluate the function f(x) = 2x2 - 3x + 7 for the input value 2.
f(x) = 2(2)2 - 3(2) + 7
= 2(4) - 3(2) + 7
What is the value of the function when x = 2?
9
10
16
17
9
When simplified and written in standard form, which quadratic function is equivalent to the polynomial shown?
2 + 7c - 4c2 - 3c + 4
-4c2 + 4c + 6
-7c2 + 10c + 6
-4c2 + 4c + 8
-7c2 + 7c + 6
-4c2 + 4c + 6
1 2 3 5 6 8 9 10
Mary throws a plastic disc to her friend, which her friend catches six seconds after Mary throws it. The table shows the height of the disc at one-second intervals.
Assuming that the throw represents projectile motion, what are the missing values in the table?
A = 5, B = 3
A = 4, B = 0
A = 4, B = 3
A = 5, B = 0
A = 4, B = 3
Which quadratic function is represented by the table?
f(x) = 3x2 + 2x - 5
f(x) = 3x2 - 2x + 5
f(x) = 2x2 + 3x - 5
f(x) = 2x2 - 2x + 5
f(x) = 3x2 - 2x + 5
Consider the quadratic function f(y) = 8y2 - 7y + 6. What is the constant of the function?
6
What is f(-3) for the function f(a) = -2a2 - 5a + 4?
1
Which quadratic function has a leading coefficient of 2 and a constant term of -3?
f(x) = 2x3 - 3
f(x) = -3x2 - 3x + 2
f(x) = -3x3 + 2
f(x) = 2x2 + 3x - 3
f(x) = 2x2 + 3x - 3
Which represents a quadratic function?
f(x) = 2x3 + 2x2 - 4
f(x) = -7x2 - x + 2
f(x) = -3x + 2
f(x) = 0x2 + 3x - 3
f(x) = -7x2 - x + 2
What is true about the function h(x) = x2 + 20x - 17? Check all that apply.
The vertex of h is (-10, -117).
The vertex form of the function is h(x) = (x + 20)2 - 17.
The maximum value of the function is -17.
To graph the function h, shift the graph of f(x) = x2 left 10 units and down 117 units.
The axis of symmetry of function h is x = 20.
The vertex of h is: (-10, -117).
To graph the function h, shift the graph of f(x) = x² left 10 units and down 117 units.
The function g(x) = 3x2 − 12x + 7 written in vertex form is g(x) = 3(x − 2)2 − 5. What is the vertex of g(x)?
(−6, −5)
(−2, −5)
(2, −5)
(6, −5)
(2, −5)
The function g(x) = -x2 + 16x - 44 written in vertex form is g(x) = -(x - 8)2 + 20. Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = -x2 + 16x - 44?
The graph of f(x) = x2 is widened.
The graph of f(x) = x2 is shifted left 8 units.
The graph of f(x) = x2 is shifted down 44 units.
The graph of f(x) = x2 is reflected over the x-axis.
The graph of f(x) = x2 is reflected over t
The function h(x) = -2x2 + 8x written in vertex form is h(x) = -2(x - 2)2 + 8. The function h(x) is shown on the graph along with the parent function, f(x) = x2.
Which statement is true concerning the vertex and axis of symmetry of h(x)?
The vertex is at (0, 0) and the axis of symmetry is x = 2.
The vertex is at (0, 0) and the axis of symmetry is y= 2.
The vertex is at (2, 8) and the axis of symmetry is x = 2.
The vertex is at (2, 2) and the axis of symmetry is y = 2.
The vertex is at (2, 8) and the axis of symmetry is x = 2.
Which function has a minimum and is transformed to the right and down from the parent function, f(x) = x2?
g(x) = -9(x2 + 2x + 1) - 7
g(x) = 4(x2 - 6x + 9) + 1
g(x) = -3(x2 - 8x + 16) - 6
g(x) = 8(x2 - 6x + 9) - 5
g(x) = 8(x2 - 6x + 9) - 5
The function g(x) = -3x2 - 36x - 60 written in vertex form is g(x) = -3(x + 6)2 + 48. Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = -3x2 - 36x - 60?
The graph of f(x) = x2 is made narrower.
The graph of f(x) = x2 is shifted right 6 units.
The graph of f(x) = x2 is shifted down 48 units.
The graph of f(x) = x2 is reflected over the y-axis.
The graph of f(x) = x2 is made narrower.
Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = 4x2 + 24x + 30?
The graph of f(x) = x2 is widened.
The graph of f(x) = x2 is shifted left 3 units.
The graph of f(x) = x2 is shifted up 30 units.
The graph of f(x) = x2 is reflected over the x-axis.
The graph of f(x) = x2 is shifted left 3 units.
What is f(x) = 8x2 + 4x written in vertex form?
f(x) = 8 -
f(x) = 8 -
f(x) = 8 - 2
f(x) = 8 - 4
A
What is f(x) = 2x2 + 28x - 5 written in vertex form?
f(x) = 2(x + 7)2 - 19
f(x) = 2(x + 7)2 - 103
f(x) = 2(x + 14)2 - 14
f(x) = 2(x + 14)2 - 98
f(x) = 2(x + 7)2 - 103
The first three steps in writing f(x) = 40x + 5x2 in vertex form are shown.
Write the function in standard form. f(x) = 5x2 + 40x
Factor a out of the first two terms. f(x) = 5(x2 + 8x)
Form a perfect square trinomial. = 16
f(x) = 5(x2 + 8x + 16) - 5(16)
What is the function written in vertex form?
f(x) = 5(x + 4) - 80
f(x) = 5(x + 8) - 80
f(x) = 5(x + 4)2 - 80
f(x) = 5(x + 8)2 - 80
f(x) = 5(x + 4)2 - 80
The function g(x) = 10x2 - 100x + 213 written in vertex form is g(x) = 10(x - 5)2 - 37. Which statements are true about g(x)? Check all that apply.
The axis of symmetry is the line x = -5.
The vertex of the graph is (5, -37).
The parabola has a minimum.
The parabola opens up.
The value of a, when the equation is written in vertex form, is negative.
The vertex of the graph is (5, -37).
The parabola has a minimum.
The parabola opens up.
Which function in vertex form is equivalent to f(x) = x2 + 6x + 3?
f(x) = (x + 3)2 + 3
f(x) = (x + 3)2 − 6
f(x) = (x + 6)2 + 3
f(x) = (x + 6)2 − 6
f(x) = (x + 3)2 − 6
Which zero pair could be added to the function so that the function can be written in vertex form?
3, -3
6, -6
9, -9
36, -36
36, -36
Which function in vertex form is equivalent to f(x) = 4 + x2 - 2x?
f(x) = (x - 1)2 + 3
f(x) = (x - 1)2 + 5
f(x) = (x + 1)2 + 3
f(x) = (x + 1)2 + 5
f(x) = (x - 1)2 + 3
Which value is needed to create a perfect square trinomial from the expression x2 + 8x + _____?
16
The function f(x) = x2 + 10x - 3 written in vertex form is f(x) = (x + 5)2 - 28. What are the coordinates of the vertex?
(-5, -28)
(-5, 28)
(5, -28)
(5, 28)
(-5, -28)
Which statements are true about the graph of the function f(x) = 6x - 4 + x2? Check all that apply.
The vertex form of the function is f(x) = (x - 2)2 + 2.
The vertex of the function is (-3, -13).
The axis of symmetry for the function is x = 3.
The graph increases over the interval (-3, ).
The function does not cross the x-axis.
The vertex of the function is (-3, -13).
The graph increases over the interval (-3, ).
What value for c will make the expression a perfect square trinomial?
x2 - 7x + c
49/4
Charla wants to determine the vertex of the function f(x) = x2 - 18x + 60 by changing the function into vertex form. Which statement about the vertex of the function is true?
The x-coordinate of the vertex is greater than the y-coordinate.
The x-coordinate of the vertex is negative.
The y-coordinate of the vertex is greater than the y-intercept.
The y-coordinate of the vertex is positive.
The x-coordinate of the vertex is greater than the y-coordinate.
How many unit tiles need to be added to the expression
x2 + 4x + 3 in order to form a perfect square trinomial?
1
Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = -8x + x2 + 7 ?
left 4, down 9
left 4, up 23
right 4, down 9
right 4, up 23
right 4, down 9
The function g(x) is a translation of f(x) = (x + 3)2 - 10. The axis of symmetry of g(x) is 5 units to the right of f(x) . Which function could be g(x)?
g(x) = (x - 2)2 + k
g(x) = (x + 8)2 + k
g(x) = (x - h)2 - 5
g(x) = (x - h)2 - 15
g(x) = (x - 2)2 + k
Which function has a vertex on the y-axis?
f(x) = (x - 2)2
f(x) = x(x + 2)
f(x) = (x - 2)(x + 2)
f(x) = (x + 1)(x - 2)
f(x)= (x-2)(x+2)
What is the y-value of the vertex of the function f(x) = -(x + 8)(x - 14)?
The y-value of the vertex is
y = 121
Gerald graphs the function f(x) = (x - 3)2 - 1. Which statements are true about the graph? Check all that apply.
The domain is {x| x ≥ 3}.
The range is {y| y ≥ -1}.
The function decreases over the interval (-∞, 3).
The function increases over the interval (-1, ∞).
The axis of symmetry is x = -1.
The vertex is (3, -1).
The range is {y| y ≥ -1}.
The function decreases over the interval (-∞, 3).
The vertex is (3, -1).
Which function has a vertex on the y-axis?
f(x) = (x - 2)2
f(x) = x(x + 2)
f(x) = (x - 2)(x + 2)
f(x) = (x + 1)(x - 2)
f(x) = (x - 2)(x + 2)
The function f(x) = x2 is translated 7 units to the left and 3 units down to form the function g(x). Which represents g(x)?
g(x) = (x − 7)2 − 3
g(x) = (x + 7)2 − 3
g(x) = (x − 3)2 − 7
g(x) = (x − 3)2 + 7
g(x) = (x + 7)2 − 3
Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 - 10x +2?
right 5, down 23
left 5, down 23
right 5, up 27
left 5, up 27
right 5, down 23
The graph of the function f(x) = (x + 2)(x − 4) is shown.
Which describes all of the values for which the graph is negative and increasing?
all real values of x where x < −2
all real values of x where −2 < x < 4
all real values of x where 1 < x < 4
all real values of x where x < 0
all real values of x where 1 < x < 4
What is the axis of symmetry of h(x) = 6x2 − 60x + 147?
x = −5
x = −3
x = 3
x = 5
x = 5
Which translation maps the graph of the function f(x) = x2 onto the function g(x) = x2 − 6x + 6?
left 3 units, down 3 units
right 3 units, down 3 units
left 6 units, down 1 unit
right 6 units, down 1 unit
right 3 units, down 3 units
The graph of the function f(x) = −3x2 − 3x + 6 is shown. Which statements describe the graph? Check all that apply.
The vertex is the maximum value.
The axis of symmetry is x = .
The domain is all real numbers.
The range is all real numbers.
The x-intercepts are at (−2, 0) and (1,0).
The function is decreasing from (−∞, 6.75).
The vertex is the maximum value.
The axis of symmetry is x = .
The domain is all real numbers.
The x-intercepts are at (−2, 0) and (1,0).
What is the y-value of the vertex of the function f(x) = -(x - 3)(x + 11)?
The y-value of the vertex is
49
What are the x-intercepts of the graph of the function f(x) = x2 + 5x − 36?
(−4, 0) and (9, 0)
(4, 0) and (−9, 0)
(−3, 0) and (12, 0)
(3, 0) and (−12, 0)
(4, 0) and (−9, 0)
Recommended textbook explanations
Advanced Mathematics: Precalculus With Discrete Mathematics and Data Analysis
1st Edition
Brown
4,885 explanations
Beginning Algebra
11th Edition
John Hornsby, Margaret L. Lial, Terry McGinnis
6,549 explanations
Larson Precalculus with Limits: A Graphing Approach
5th Edition
Bruce H. Edwards, Larson, Robert P. Hostetler
9,232 explanations
Core Connections Integrated 3
1st Edition
Brian Hoey, Judy Kysh, Leslie Dietiker, Tom Sallee
1,628 explanations
Sets with similar terms
Completing the Square
10 terms
The Cube Root Function
10 terms
Sets found in the same folder
Quadratic Functions Unit Test
67 terms
Algebra 1 - E2020 Unit Test
26 terms
Quadratic Functions: Vertex Form
15 terms
Unit Test Unit Test Review quadratic equations
15 terms
Other sets by this creator
Study Guide Questions - Fahrenheit 451
25 terms
Civics Chapter 3 Questions
30 terms
The Scarlet Ibis, "The Scarlet Ibis"
99 terms
La vaca y el mono
8 terms
Verified questions
ALGEBRA
Solve each formula for the indicated variable. R(r1 + r2) = r1r2, for R
ALGEBRA
There are 14 boys and 18 girls in a class. The teacher allows the students to vote whether they want to take a test on Friday or on Monday. A total of 6 boys and 10 girls vote to take the test on Friday. Organize the information in a two-way table. Then find and interpret the marginal frequencies.
BUSINESS MATH
Suppose $600 is deposited into an account every quarter. The account earns 5% interest, compounded quarterly. What is the future value of the account after 5 years?
ALGEBRA2
Two number cubes are rolled—one blue and one yellow. Explain why the events are dependent. Then find the indicated probability. The blue cube is less than 3 and the product is 8.
Other Quizlet sets
American Government and Phases
19 terms
History 201 Exam 3
78 terms
Module quiz prep
25 terms
Contemporary Environmental Issues Midterm
122 terms
Related questions
QUESTION
What is a solution to an equation
QUESTION
Simplify 5m - 13n - n + 4m.
QUESTION
Declare a variable isACustomer , suitable for representing a true or false value .
QUESTION
Miranda is conducting a poll to determine how many students would attend a students-only school dance if one was held. Which sample is most likely to yield a representative sample for the poll?