3.2 Quadratic Functions--Connecting Intercepts and Linear Factors (Due 11/14/24)
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Last updated 12 months ago
56 questions
Day 1 11/5/24
Essential Question: How are the x-intercepts of a quadratic function and its linear factors related?
Learning Target: Students will be able to identify the x-intercepts of quadratic equations and use them to create graphical representations of those functions.
Show your work for credit.
Required
10 points
10
Question 1
1.
Guided Practice:
Connecting intercepts and factors
Graph the Function y=(x − 3)(x + 5)
Where does the parabola intercept (cross) the x-axis?
x=_______ and x=_______
Required
5 points
5
Question 2
2.
Connecting intercepts and factors
Graph the Function y=(x + 6)(x - 1)
Where does the parabola intercept (cross) the x-axis?
x=_______ and x=_______
Required
5 points
5
Question 3
3.
Connecting intercepts and factors
Graph the Function y=2(x - 8)(x - 8)
Where does the parabola intercept (cross) the x-axis?
x=_______
Required
10 points
10
Question 4
4.
Connecting intercepts and factors
Graph the Function y=-6(x + 3)(x)
Where does the parabola intercept (cross) the x-axis?
x=_______ and x=_______
Required
10 points
10
Question 5
5.
Graph the Function y=(x + 6)(x + 2)
1) What are the x-intercepts? (Where the graph crosses the x-axis)
x=_______ and x=_______
2) What is the axis of symmetry? (The middle of the parabola, put your hands together)
x=_______
Required
10 points
10
Question 6
6.
Graph the Function y=(x - 6)(x + 2)
1) What are the x-intercepts? (Where the graph crosses the x-axis)
x=_______ and x=_______
2) What is the axis of symmetry? (The middle of the parabola, put your hands together)
x=_______
Required
10 points
10
Question 7
7.
Graph the Function y=2(x + 7)(x - 3)
1) What are the x-intercepts? (Where the graph crosses the x-axis)
x=_______ and x=_______
2) What is the axis of symmetry? (The middle of the parabola, put your hands together)
x=_______
Required
10 points
10
Question 8
8.
Graph the function y=(x - 4)(x - 2). What is the relationship between the axis of symmetry and its intercepts?
Required
20 points
20
Question 9
9.
Guided Practice
Graph the function using its intercepts.
Required
10 points
10
Question 10
10.
Graph the function using its intercepts.
Required
10 points
10
Question 11
11.
Graph the function using its intercepts.
Required
15 points
15
Question 12
12.
Guided Practice: Graphing and Interpreting Quadratic Functions
The height of a football after it has been kicked from the top of a hill can be modeled by the equation:
Where h is the height of the football in feet and t is the time in seconds.
How long is the football in the air?_______
How high does the football get?_______
Graph the function to answer the question.
Required
10 points
10
Question 13
13.
Graph the function using its intercepts.
15 points
15
Question 14
14.
Graphing and Interpreting Quadratic Functions:
The height of a flare fired from the deck of a ship can be modeled by h = (−4t + 24)(4t + 4) where h is the height of the flare above water in feet and t is the time in seconds.
Find the number of seconds it takes the flare to hit the water._______
How many seconds does it take to reach its highest point?_______
Graph the function to answer the question.
Required
10 points
10
Question 15
15.
Exit Ticket
What is the connection between the x-intercepts of the function y = (x − 3)(x + 5) and the factors: (x − 3) and (x + 5)? Think about the graph of y = (x - 3)(x + 5)
Day 2 11/6/24
Review
Required
10 points
10
Question 16
16.
Solve this linear equation.
Required
10 points
10
Question 17
17.
Solve this linear equation.
Solving Quadratic Equations by Graphing
Required
10 points
10
Question 18
18.
Solve this quadratic equation graphing
x=_______
x=_______
Required
10 points
10
Question 19
19.
Solve this quadratic equation graphing.
x=_______
x=_______
Required
10 points
10
Question 20
20.
Solve this quadratic equation graphing.
x=_______
x=_______
Required
10 points
10
Question 21
21.
Solve this quadratic equation graphing.
x=_______
x=_______
Required
10 points
10
Question 22
22.
Solve this quadratic equation graphing.
x=_______
x=_______
Required
10 points
10
Question 23
23.
Solve this quadratic equation graphing.
x=_______
x=_______
Required
10 points
10
Question 24
24.
Solve this quadratic equation graphing.
x=_______
x=_______
Required
10 points
10
Question 25
25.
Solve this quadratic equation graphing.
x=_______
x=_______
Required
20 points
20
Question 26
26.
A bird is in a tree 30 feet off the ground and drops a twig that lands on a
rosebush 25 feet below. The function h (t) = -16t²+ 30, where t represents the time
in seconds, gives the height h, in feet, of the twig above the ground as it falls. When
will the twig land on the bush?
Solve this quadratic equation graphing.
t=_______
Required
20 points
20
Question 27
27.
A trampolinist steps off from 15 feet above ground to a trampoline 13 feet
below. The function h (t) = -16 t²+ 15, where t represents the time in seconds, gives
the height h, in feet, of the trampolinist above the ground as he falls. When will the
trampolinist land on the trampoline? (Round your answer to the nearest hundredth)
t=_______
Graph the quadratic equation to help you answer the question.
Day 3 11/7/24
Essential Question: How are the x-intercepts of a quadratic function and its linear factors related?
Learning Target: Students will be able to identify the x-intercepts of quadratic equations and use them to create graphical representations of those functions.
Show your work for credit.
Required
20 points
20
Question 28
28.
Graph each quadratic function and each of its linear factors. Then identify the x-intercepts and the axis of symmetry of each parabola.
Left x-intercept (use coordinate form)
_______
Right x-intercept (use coordinate form)
_______
Axis of Symmetry (use x=___ form)
_______
Vertex (use coordinate form)
_______
Required
20 points
20
Question 29
29.
Graph each quadratic function and each of its linear factors. Then identify the x-intercepts and the axis of symmetry of each parabola.
Left x-intercept (use coordinate form)
_______
Right x-intercept (use coordinate form)
_______
Axis of Symmetry (use x=___ form)
_______
Vertex (use coordinate form)
_______
Required
20 points
20
Question 30
30.
Graph each quadratic function and each of its linear factors. Then identify the x-intercepts and the axis of symmetry of each parabola.
Left x-intercept (use coordinate form)
_______
Right x-intercept (use coordinate form)
_______
Axis of Symmetry (use x=___ form)
_______
Vertex (use coordinate form)
_______
Required
20 points
20
Question 31
31.
Graph each quadratic function and each of its linear factors. Then identify the x-intercepts and the axis of symmetry of each parabola.
Left x-intercept (use coordinate form)
_______
Right x-intercept (use coordinate form)
_______
Axis of Symmetry (use x=___ form)
_______
Vertex (use coordinate form)
_______
Required
20 points
20
Question 32
32.
Graph each quadratic function and each of its linear factors. Then identify the x-intercepts and the axis of symmetry of each parabola.
Left x-intercept (use coordinate form)
_______
Right x-intercept (use coordinate form)
_______
Axis of Symmetry (use x=___ form)
_______
Vertex (use coordinate form)
_______
Required
20 points
20
Question 33
33.
Graph each quadratic function and each of its linear factors. Then identify the x-intercepts and the axis of symmetry of each parabola.
Left x-intercept (use coordinate form)
_______
Right x-intercept (use coordinate form)
_______
Axis of Symmetry (use x=___ form)
_______
Vertex (use coordinate form)
_______
Day 4 11/8/24
Warm-Up: Spiral Review
Required
10 points
10
Question 34
34.
Mutlitply the binomials:
Required
10 points
10
Question 35
35.
Mutlitply the binomials:
Factoring Quadratics
Required
10 points
10
Question 36
36.
Factor each expression. Be sure to check for a GCF first.
Required
10 points
10
Question 37
37.
Factor each expression. Be sure to check for a GCF first.
Required
10 points
10
Question 38
38.
Factor each expression. Be sure to check for a GCF first.
Required
10 points
10
Question 39
39.
Factor each expression. Be sure to check for a GCF first.
Spiral Review
Required
10 points
10
Question 40
40.
Solve this equation:
6x-9=45
Required
10 points
10
Question 41
41.
What does is it mean to solve an equation?
Solving Quadratics
Required
10 points
10
Question 42
42.
Solve the following Quadratic function:
(2x + 3)(x + 1) = 0
x=_______
x=_______
Required
10 points
10
Question 43
43.
Solve the following Quadratic function:
x(8x + 3) = 0
x=_______
x=_______
Required
10 points
10
Question 44
44.
Solve the following Quadratic function:
(x - 7)(x + 7) = 0
x=_______
x=_______
Required
10 points
10
Question 45
45.
Solve the following Quadratic function:
2x2 + 5x + 2 = 0
x=_______
x=_______
Required
10 points
10
Question 46
46.
Solve the following Quadratic function:
3x2 + 22x + 35 = 0
x=_______
x=_______
Required
10 points
10
Question 47
47.
Solve the following Quadratic function:
7x2 - 60x + 32 = 0
x=_______
x=_______
Required
10 points
10
Question 48
48.
Factor and solve:
3x2 - x - 14 = 0
x=_______
x=_______
Required
10 points
10
Question 49
49.
Factor and solve:
3x2 + 17x - 28 = 0
x=_______
x=_______
Solving Quadratic Word Problem
Calculating Room Areas
People frequently need to calculate the area of rooms, boxes or plots of land. An example might involve building a rectangular box where one side must be twice the length of the other side.
For example, if you have only 4 square feet of wood to use for the bottom of the box, with this information, you can create an equation for the area of the box using the ratio of the two sides. This means the area -- the length times the width -- in terms of x would equal x times 2x, or 2x2. This equation must be less than or equal to four to successfully make a box using these constraints.
Required
10 points
10
Question 50
50.
For each rectangle with area given, determine the binomial factors that describe the dimensions.
Length
_______
Width
_______
Required
10 points
10
Question 51
51.
For each rectangle with area given, determine the binomial factors that describe the dimensions.
Length
_______
Width
_______
Required
10 points
10
Question 52
52.
Find the length and width of a rectangle whose length is 5 cm longer than its width and whose area is 50 cm².
length
_______
width
_______
Required
10 points
10
Question 53
53.
The width of a rectangle is six
meters less than its length. If the
area of the rectangle is 112 m² , find
the dimensions of the rectangle.
Width
_______
Length
_______
Required
10 points
10
Question 54
54.
The length of a rectangle is one
foot more than twice its width. If
the area of the rectangle is 300 ft²,
find the dimensions of the rectangle.
Width=_______
Length=_______
Objects Affected by Gravity
Required
30 points
30
Question 55
55.
Jason jumped off a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function h(t) = -16t²+ 16t + 480 , where t is the time in seconds and h is the height in feet.
How long did it take for Jason to reach his maximum height?_______
What was the highest point that Jason reached?_______
Jason hit the water after how many seconds?_______
Required
40 points
40
Question 56
56.
If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h after t seconds is given by the equations h(t) = -16t²+ 128t (if air
resistance is neglected).
How long will it take for the rocket to return to the ground?_______
After how many seconds will the rocket be 112 feet above the ground?_______
How long will it take the rocket to hit its maximum height?_______