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WorksheetsQuadratic Functions and Graphs
Total questions: 42
Worksheet time: 29mins
1. The graph of a quadratic function is shown below: Find the following key features about the quadratic function: The vertex is: ______ The equation of axis of symmetry is: ______ The vertex is at a ______ (maximum or minimum) value of ______
The vertex: (-2, -1), The equation of axis of symmetry is: x =- 2, The vertex is at a minimum value of -11
The vertex: (-1, -4), The equation of axis of symmetry is: x = -1, The vertex is at a maximum value of -4
The vertex: (0, 0), The equation of axis of symmetry is: x = 0, The vertex is at a minimum value of 0
The vertex: (3, 2), The equation of axis of symmetry is: x = 3, The vertex is at a maximum value of 2
The graph of a quadratic function is shown below: Which statement is true based on the given graph?
The function has a zero at -8.
The maximum value of the function is -4.
The equation of the axis of symmetry of the graph is x=-4
The vertex of the graph is (-4,-2).
The graph of a quadratic function is shown below. What are the zeros of the function? Select TWO correct points that represent the solutions.
(2,0)
(3,-1)
(6,8)
(4,0)
(0,8)
The table represents some points on the graph of a quadratic function, f. Find the range of f.
All real numbers greater than or equal to 2.
All real numbers less than or equal to 2.
All real numbers greater than -19/4
All real numbers less than or equal to -19/4
Function f is defined by f(x) = 2x2+3x=5 . What are the solutions to the function?
x=-1 and x= -5/2
x=1 and x= 2/5
x=1 and x= -5/2
x=-1 and x= 2/5
What are the solutions to the equation x2−2x=19 ?
x = -1 ± √20
x = 1 ± √20
x = -2 ± √2
x = 5 ± √2
Find the positive solution of x2−6x=40 ?
x=6
x=10
x=8
x=-4
If f(x) = x2 was transformed to create the function g(x) = f(x - 2) - 3, find the vertex. (_____,_____)
(2,-3)
(0,0)
(-2,3)
(3,-2)
The quadratic function h, h(12) = 0 and h(−5/2) = 0. What is a possible equation for h in factored form? HINT: ORDER MATTERS HERE!!!!
(a)
An experiment examines the relationship between the number of miles a car travels per gallon of gasoline and the speed of the car, x, in miles per hour.
Which function best models the data? (Round to 2 decimal places)
f(x) = 0.02x² − 1.13x + 46.65
f(x) = 0.08x² − 0.10x + 45
f(x) = −0.08x² − 0.10x + 45
The graph of the function g is shown below. Which function is best represented by the graph?
g(x) = x² − 2x − 8
g(x) = −x² − 2x − 8
g(x) = −x² + 2x + 8
g(x) = x² + 2x − 8
The quadratic function f(x) = x² is transformed to create g shown below. What is the equation of g?
g(x) = f(x − 2) + 1
g(x) = 3f(x + 2) + 1
g(x) = 3f(x − 2) + 1
g(x) = f(x + 2) − 1
If the quadratic parent function f(x)= x^2 to create g(x)= f(x-1)-3. The graph of f is translated ______ by 1 unit and ______ by 3 units to create the graph of function of g.
left, down
right, up
left, up
right, down
Which quadratic function in vertex form can be represented by the graph that has a vertex at (2,10) and passes through the point (4,22)?
y = 2(x − 2)² + 10
y = 3(x − 2)² + 10
y = 2(x + 3)² − 6
y = 3(x − 3)² + 6
Find the domain of f(x) = −x² − 10x.
All real numbers
All real numbers greater than or equal to 25
All real numbers less than or equal to 25
All real numbers greater than or equal to 0 and less than or equal to 25
If f(x) = x² was reflected and shifted left 3 units and down 4 units to create g, which quadratic function represents the new graph of g?
f(x) = −(x + 4)² − 3
f(x) = −(x + 3)² − 4
f(x) = (x + 3)²
f(x) = −(x − 4)²
How old is Ms. Cerda?
(a)
Ms. Cap is a millennial.
Ms. Cerda graduated from Wunsche HS in 2022.
What is Ms. Cap’s favorite football team?
Steelers
Texans
Bills
Cowboys
What college does Ms. Cerda attend?
University of Houston
Sam Houston State University
Texas Tech University
University of Houston-Downtown
Domain is….
x
y
Range is…
x
y
What is another word for solutions? (Select TWO answers)
x-interecepts
y-intercepts
zeros
Ms. Cap has 3 dogs.
Who is taller?
Ms. Cap
Ms.Cerda
What does G.O.A.T stand for?
goat of all time
greatest of all time
greatest of all teachers
gifted overachiever and thinker
f(x) is a fancy way of saying….
x
y
This is a baby picture of Ms. Cap
Who is this baby?
Ms. Cerda
Ms. Cap
AI Generated
Google Photo
Ms. Cap’s natural hair color is blonde
Ms. Cap has been teaching for 13 years.
This is a picture of Ms. Cerda.
True
False
What is Ms. Cerda’s dog’s name?
Clutch
El Chavo
Max
Bob
Where is this cat from?
Ms. Cerda
Ms. Cap
AI generated
This cat is AI generated.
Find the domain of the graph.
All real numbers.
All real numbers greater than or equal to -3.
All real numbers less than or equal to -3.
All real numbers greater than or equal to 0.
Find the range of the graph.
All real numbers.
All real numbers greater than or equal to -3.
All real numbers less than or equal to -3.
All real numbers less than 0.
The red graph shifted where?
down by 2
up by 1
down by 1
up by 2
The RED graph shifted where?
left by 1
right by 1
down by 1
up by 1
How many solutions does the graph have?
1
none
2
What is the y-intercept on the graph?
(0,-3)
(-3,0
(0,0)
(0,3)
