Unit 6 – Understanding Quadratic Functions
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Unit 6 Assignment 1 – What is a Quadratic Function? (FOUR sided fence problem)
Directions: ON YOUR OWN PAPER, simplify the following quadratic equations and rewrite them in standard form. After
rewritten, identify the 𝒂, 𝒃, and 𝒄 terms.
1) ℎ(𝑡) = −𝑡(16𝑡 + 7)
2) 𝐴(𝑠) = 100𝑠 − 2𝑠 2
3) 𝑔(𝑥) = 3𝑥 2 + 2𝑥 − 1
4) 𝑓(𝑥) = 𝑥(𝑥 + 3)
5) 𝑓(𝑥) = 3𝑥(𝑥 − 8) + 5
6) 𝑔(𝑠) = (𝑠 + 4)𝑠 − 2
7) 𝑑(𝑡) = (20 + 3𝑡)𝑡
8) 𝑚(𝑠) =
𝑠(𝑠+3)
4
9) 𝑓(𝑛) =
2𝑛(3𝑛−6)
3
Directions: Given the story problem, find and fill in all other information to depict the problem as a function, table and graph.
10) Aiko is enclosing a new rectangular flower garden with a rabbit garden fence. She has 40 feet of fencing.
Equation for total perimeter:
Table of values:
Window 𝑥: [−5,25], 𝑦: [−20,150]
𝑥𝑠𝑐𝑙: 5, 𝑦𝑠𝑐𝑙: 20
𝐴(𝑤)
𝑤
Length in terms of width:
𝑙=
𝐴(𝑤) = 𝑤(
Standard form:
𝐴(𝑤) =
−𝑤)
𝑤2 +
0
5
10
15
20
25
Maximum: (_____, _____)
11) Pedro is building a rectangular sandbox for the community park. The materials available limit the perimeter of the
sandbox to 100 feet.
Equation for total perimeter:
Table of values:
Window 𝑥: [−10,60], 𝑦: [−50,700]
𝑥𝑠𝑐𝑙: 10, 𝑦𝑠𝑐𝑙: 100
Length in terms of width:
𝑙=
𝐴(𝑤) = 𝑤(
Standard Form:
𝐴(𝑤) =
−𝑤)
𝑤2 +
𝑤
0
10
20
30
40
50
60
𝐴(𝑤)
Maximum: (_____, _____)
12) Nelson is building a rectangular ice rink for the community park with materials to make the perimeter 250 feet.
Equation for total perimeter:
Table of values:
Window 𝑥: [−20,140], 𝑦: [−500,4500]
𝑥𝑠𝑐𝑙: 20, 𝑦𝑠𝑐𝑙: 5000
Length in terms of width: 𝑙 =
𝐴(𝑤) = 𝑤(
Standard form:
𝐴(𝑤) =
−𝑤)
𝑤2 +
𝑤
0
20
40
60
80
100
120
140
160
𝐴(𝑤)
Maximum: (_____, _____)
CONTINUED ON NEXT PAGE >>>>>>>
Unit 6 – Understanding Quadratic Functions
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Directions: Use your knowledge to set up equations and solve for the variables.
13)
14) Angle A is complementary to angle
B, and angle B is three times bigger
than C. If C measures 8°, what is
the measure of angle A?
15)
16)
17) 34) A boat skipper at sea notices a
148 meter tower on shore. He
determines the angle of elevation
to the top of the tower to be 9
degrees. How far is he from the
shore?
18)
19)
20) The quadrilateral is a kite.
̅̅̅̅ = 4𝑐𝑚, 𝑚𝐵𝐶
̅̅̅̅ = 7𝑐𝑚, find
21) 𝑚𝐴𝐵
̅̅̅̅ .
𝑚𝐴𝐶
Directions: Evaluate the function for the given value(s).
22) 𝑓(𝑥) = 3𝑥 2 + 4𝑥
𝑓(2) =
𝑓(−3) =
23) 𝑔(𝑥) = 𝑥(90 − 𝑥)
𝑔(10) =
𝑔(14.5) =
24) ℎ(𝑥) =
ℎ(8) =
ℎ(−2) =
2𝑛+4
8𝑛
Unit 6 Assignment 2 – Linear vs. Quadratic (THREE sided fence problem)
Directions: Graph each set of values and determine whether the function is linear, quadratic, or exponential.
1)
2)
𝒙
-4
-2
0
2
4
𝒚
7
6
5
4
3
𝒙
-1
0
1
2
3
𝒚
-2.5
-2
-1
1
5
The function is:
The function is:
I know because…
I know because…
3)
4)
𝒙
-2
0
2
4
6
𝒚
-8
0
4
4
0
𝒙
-3
-2
-1
0
1
𝒚
-2
0
2
4
6
The function is:
The function is:
I know because…
I know because…
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Unit 6 – Understanding Quadratic Functions
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Directions: NO CALCULATOR!!! Determine whether the function is linear, quadratic or exponential. Explain your reasoning.
6) 𝑓(𝑥) = −2𝑠 2 + 4
5) 𝑦 = 3𝑥 + 4
7) 𝑦 = 5𝑥(𝑥 − 2)
𝑦 = 3𝑥 2 + 3(𝑥 − 𝑥 2 ) + 1
8)
Directions: MULTIPLE CHOICE PRACTICE. Choose the best answer from the list of possible answers.
9)
10) What type of function is 𝑔(𝑥) = 3(𝑥 − 1) + 5
a. Quadratic
b. Linear
c. Exponential
d. Step
Which of the following is NOT a quadratic function?
a. 𝑎(𝑥) = 4𝑥 2
b. 𝑏(𝑥) = (𝑥 + 1)𝑥
c. 𝑐(𝑥) = 𝑥 2 + 2𝑥 − 𝑥 2 + 1
d. 𝑑(𝑥) = (𝑥 − 2)(𝑥 + 8)
Directions: The Quickgrow Fertilizer Company is working on different formulas for flower fertilizers. The table shows the growth of unfertilized plant A
and the growth of a fertilized plant B.
Time
(days)
0
1
2
3
4
5
6
Height of
plant A (cm)
4
6
8
10
12
14
16
Height of
plant B (cm)
3
4
6
9
13
18
24
11) Which plant height (plant A or plant B)
would be represented by a linear
function?
12) Which plant height would represent a
quadratic function?
14) Would the function 𝐴(𝑥) =
−2𝑥 + 4 or the function
𝐴(𝑥) = 2𝑥 + 4 represent the
growth of plant A.
15) Explain your reasoning.
13) Explain your reasoning.
Directions: Write a quadratic function in standard form that represents each area as a function of the width.
16) A builder is designing a rectangular parking lot. She has 300 feet of fencing to enclose the parking lot around 3 sides.
], 𝑦: [
]
Equation for total perimeter:
Table of values:
Window 𝑥: [
,
,
𝑥𝑠𝑐𝑙: _________, 𝑦𝑠𝑐𝑙: __________
Length in terms of width: 𝑙 =
𝐴(𝑤) = 𝑤(
Standard form:
𝐴(𝑤) =
−2𝑤)
𝑤2 +
𝑤
0
20
40
60
80
100
120
140
160
𝐴(𝑤)
Maximum: (_____, _____)
17) Joe is looking to put a fence around his garden to keep the wildlife from eating his prized tomatoes. The garden is
next to the barn, so he will only need three sides of fencing to enclose his garden. He has 100 feet of fencing to use.
], 𝑦: [
]
Equation for total perimeter:
Table of values:
Window 𝑥: [
,
,
𝑥𝑠𝑐𝑙: 10, 𝑦𝑠𝑐𝑙: __________
Length in terms of width: 𝑙 =
𝐴(𝑤) = 𝑤(
Standard form:
𝐴(𝑤) =
−2𝑤)
𝑤2 +
𝑤
0
10
20
30
40
50
60
70
80
𝐴(𝑤)
Maximum: (_____, _____)
Unit 6 – Understanding Quadratic Functions
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18) Amanda is building a fence for her orange flower garden. She needs to fence ALL FOUR SIDES and has 2500 feet of
fencing. Help her figure out the best configuration.
], 𝑦: [
]
Equation for total perimeter:
Table of values:
Window 𝑥: [
,
,
𝑤
𝐴(𝑤)
Length in terms of width: 𝑙 =
𝐴(𝑤) =
Standard form:
𝐴(𝑤) =
Maximum: (_____, _____)
19) Amanda is also needing to build a cage for her pet hedgehog named Penelope. Amanda wants to be sure Penelope
is protected so she will be putting one side of the cage against the house, so she only needs to use her 20 feet of
cage material to make a 3 sided enclosure.
], 𝑦: [
]
Equation for total perimeter:
Table of values:
Window 𝑥: [
,
,
𝑤
𝐴(𝑤)
Length in terms of width: 𝑙 =
𝐴(𝑤) =
Standard form:
𝐴(𝑤) =
Maximum: (_____, _____)
Directions: Review problem like the last of the notes that Chris did for unit 6!
20) Write the equation of graph of circle E.
21) Draw the square that surrounds from
points (−1,3), (7,3), (7, −5), (−1, −5)
24) Find area inside square, but outside
circle.
25) What is the arc length the LONG way
from points (−7, −1) to (3,3)?
22) Find the area of the entire square.
23) Find the entire area of the circle.
27)
26) Find the SMALLER sector area from
points (−7, −1) to (3,3).
Unit 6 Writing Prompt #1 (found on last page of your packet!)
Unit 6 – Understanding Quadratic Functions
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Unit 6 Assignment 3 – Attributes of Quadratic Functions
Quickgrow Fertilizer is also experimenting with a fertilizer that is supposed to increase yield of pepper plants.
The yield for plant C can be represented by the function 𝐶(𝑥) = −12.5𝑥 + 100. The yield for plant D can be
represented by the function 𝐷(𝑥) = −3𝑥 2 + 21𝑥 + 50. The graphs for both plants are shown.
1) Label the funcitons correctly as to 4) Determine the x-intercept(s) of
which is plant C and which is plant
each function and describe the
D.
meaning in terms of the problem
situation.
2) How do you know which to label
as C and D?
5) Determine the maximum of the
3) Determine the y-intercept(s) of
quadratic function. Explain what
each function and describe the
it means in terms of yield for plant
MEANING of each in terms of the
D.
problem situation.
Directions:
Directions: Write a function that represents the vertical motion described in each problem situation. Then find the maximum, write the coordinates,
and write a sentence to describe what the x and y coordinates mean in terms of the problem situation. Finally, find the zeros of the function and
explain what they mean in terms of the problem situation.
Example: A soccer ball is thrown from a
height of 25 feet at an initial velocity of 46
feet per second.
ℎ(𝑡) = −16𝑡 2 + 46𝑡 + 25
max: (1.44,58.06), this means the ball is
at its maximum height of 58.06 feet after
1.44 seconds.
Zeros: (−0.47,0) and (3.34,0) The first
zero means nothing because time can’t be
0, but the second means the soccer ball
touches back down after 3.34 seconds.
6)
A catapult hurls a watermelon from a
height of 36 feet at an initial velocity
of 82 feet per second.
7)
A catapult hurls a cantaloupe from a
height of 12 feet at an initial velocity
of 47 feet per second.
8)
A basketball is thrown from a height
of 7 feet at an initial velocity of 54
feet per second.
9)
A football is thrown from a height of 6
feet at an initial velocity of 74 feet per
second.
Directions: MULTIPLE CHOICE PRACTICE. Choose the best answer from the list of possible answers.
y
10) The equation o this graph in
11) Which statement is NOT TRUE about the

standard form would be?
function of the parabola 𝑦 = −𝑥 2 + 4

a) −2𝑥 2 + 2
b) (𝑥 + 2)(𝑥 − 2)
c) 𝑥 2 − 2
1 2
d)
𝑥 −2
2


   
x







(graphed to the left)?
a) The 𝑥-intercepts are (−2,0) and (2,0).
b) The 𝑦-intercept is 4.
c) The vertex is at (0,4).
d) The minimum value is 4.

Directions: You will find a set of three functions below. One will be linear, one will
 be exponential, and one will be quadratic. List the characteristics in
each table that helped you to identify each type of function. If possible, write the function that belongs with the tables.
12)
𝑓(𝑥)
𝑥
6
64
7
128
8
256
9
512
10 1024
L, Q or E?
Why?
𝑓(𝑥) =________
𝑔(𝑥)
𝑥
6
36
7
49
8
64
9
81
10
100
L, Q or E?
Why?
𝑔(𝑥) =________
ℎ(𝑥)
𝑥
6
11
7
13
8
15
9
17
10
19
L, Q or E?
Why?
ℎ(𝑥) =________
13)
𝑓(𝑥)
𝑥
-2
-17
-1
-12
0
-7
1
-2
2
3
L, Q or E?
Why?
𝑓(𝑥) =________
𝑔(𝑥)
𝑥
-2
1/25
-1
1/5
0
1
1
5
2
25
L, Q or E?
Why?
𝑔(𝑥) =________
ℎ(𝑥)
𝑥
-2
9
-1
6
0
5
1
6
2
9
L, Q or E?
Why?
ℎ(𝑥) =________
CONTINUED ON NEXT PAGE >>>>>>>
Unit 6 – Understanding Quadratic Functions
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14) The citizens of Herrington County are wild about their dogs. They have an existing dog park for all dogs to play, but have decided
to build a second area for small dogs only. The plan is to build a rectangular fenced in area that will be adjacent to the existing
dog park. The sketch is shown below. The county has enough money in the budget to buy 1000 feet of fencing.
a. Determine the length of the new dog park, 𝑙, in terms of the width, 𝑤.
b. Write an equation (𝐴(𝑤)) for the area of the new park in terms of
width.
c. Does this function has an absolute minimum or maximum? Explain
your answer.
d. Sketch the graph of the function on the graph provided. Label the axes,
the absolute max/min, the x-intercepts, and the y-intercepts.
e. Explain what each of the x-intercepts means in terms of the problem
situation.
f. What should the dimensions of the dog park be to maximize the area?
What is the maximum area of the park?
g. Use the graph to determine the dimensions of the park if the area was
restricted to 105,000 square feet.
h. LABEL your graph if you haven’t already done so!
Sketch:
Directions: Determine the x-intercepts of each quadratic function in factored form.
15) 𝑓(𝑥) = (𝑥 − 2)(𝑥 − 8)
16) 𝑓(𝑥) = 𝑥(𝑥 − 6)
1
17) 2 (𝑥 + 15)(𝑥 − 4)
18) 𝑓(𝑥) = −3(2𝑥 + 1)(𝑥 − 8)
Directions: Given the figure, find the desired information.
⃡ and 𝐵𝐷
⃡ are
𝐶𝐷
tangent lines.
̅̅̅̅ = 12cm
𝑚𝐵𝐷
̅̅̅̅ = 13cm
𝑚𝐴𝐷
Directions:
19) What is the radius of circle A?
20) If drawn, what is 𝑚∠𝐵𝐴𝐷?
21) What is 𝑚∠𝐶𝐷𝐵?
Directions: Find the desired ratios of the given triangle.
Write your answers as simplified fractions.
22) Given the two equations, graph
the circles.
Circle Y: (𝑥 − 3)2 + (𝑦 − 5)2 = 1
Circle M: (𝑥 + 2)2 + (𝑦 − 8)2 = 16
23) Use the triangle above to fill in the blanks.
cos(𝐵) = ____
sin(𝐴) = ____
3
4
sin(___) =
______(𝐴) =
5
3
Unit 6 – Understanding Quadratic Functions
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Unit 6 Assignment 4 – Features Of Quadratic Functions
1) A masking tape company has to decide how many hundreds of rolls
of tape to produce each day. The company knows that the costs to
produce the tape go down the more rolls they make. However, the
overall cost to the company increases if they have to store
overstock. The company determined that the cost to produce x
hundreds of units a day could be represented by the function:
𝑓(𝑥) = 0.04𝑥 2 − 16𝑥 + 15000.
a. Graph the function. Sketch the graph and label the axes.
b. What are the domain and range of the function in terms of the
problem situation?
c. Over what interval does the cost of making the rolls of tape
decrease? Increase?
d. How many rolls of tape should the company make to minimize
cost?
e. What is this minimum cost to the company?
f. Determine the x-intercept(s) of this function and describe what they mean in terms of the cost to the company.
Directions: MULTIPLE CHOICE PRACTICE. Choose the best answer from the list of possible answers.
3) A ball is thrown vertically upward with an initial speed of 80 meters
2) If Madi grows prized roses. She wants to start a new rose
per second. The height h, in meters, above the starting point after t
garden and has 50 feet of fencing to enclosure all 4 sides of
seconds is given by the equation ℎ(𝑡) = −4.9𝑡 2 + 80𝑡. How long is
her garden. What are the dimensions that would give her the
the ball in the air?
greatest area for her new garden?
a)
b)
c)
d)
5 feet wide by 10 feet long
8 feet wide by 17 feet long
10 feet wide by 15 feet long
12.5 feet wide by 12.5 feet long
a)
b)
c)
d)
16.3 seconds
8.2 seconds
326.5 seconds
20 seconds
Directions: Given the story problems, identify the key features and answer the questions that follow. USE YOUR OWN PAPER!!!
4) Mr. Sheffield has built a toy rocket for his daughter. The rocket launches off the ground with an initial velocity of 200
feet per second.
The function:
Interval the rocket is increasing (rising):
Table of appropriate values:
Maximum Value: ( _____, ______) Interval the rocket is decreasing (falling):
Sketch a graph with key features
AND its interpretation:
shown:
Total time object is in the air:
Evaluating the function when 𝑡 = 5 give a y-value of 600. What does this mean in
terms of the problem situation?
When at 15 seconds, what is the height of the rocket? Mr. Sheffield’s last rocket reached a height of 400 feet in the air.
Is this rocket better than his last? Explain.
5) A football is punted into the air from a height of 4 feet with an initial velocity of 60 feet per second.
The function:
Interval the object is increasing (rising):
Table of appropriate values:
Maximum Value: ( _____, ______) Interval the object is decreasing (falling):
Sketch a graph with key features
AND its interpretation:
shown:
Total time object is in the air:
Evaluating the function when 𝑡 = 5 give a y-value of -96. What does this mean in
terms of the problem situation?
When at 2.5 seconds, what is the height of the football?
When does the football have a height of 40 feet?
Directions: Determine the vertex of each quadratic function in vertex form, then state whether it is a maximum or minimum.
1
6) 𝑔(𝑥) = − 2 (𝑥 − 5)2 + 4
7) 𝑓(𝑥) = 2(𝑥 + 4)2
8) 𝑓(𝑥) = −(𝑥 − 5)2
9) 𝑓(𝑥) = 𝑥 2 + 8
CONTINUED ON NEXT PAGE >>>>>>>
Unit 6 – Understanding Quadratic Functions
P a g e |8
Directions: Given the functions, describe the graph using the following characteristics: domain, range, vertex, max/min, y-intercept,
zeros, axis of symmetry, interval of increase, interval of decrease.
10)
Domain:
Range:
Vertex:
Maximum or
Minimum:
11) 𝑓(𝑥) = 2(𝑥 − 4)2 − 8
Domain:
Range:
Vertex:
Maximum or minimum:
y-intercept
Zeros:
Axis of symmetry:
Interval increasing:
Interval decreasing:
y-intercept:
zeros:
axis of
symmetry:
12) 𝑔(𝑥) = −0.1𝑥 2 + 1.2𝑥 − 16
Zeros:
Domain:
Range:
Axis of symmetry:
Interval
increasing:
Vertex:
Interval increasing:
Interval
decreasing:
y-intercept
Maximum or minimum:
Interval decreasing:
Directions: Given the story problem, find and fill in all other information to depict the problem as a function, table and graph.
13) Chanelle wants to build a child enclosure. She has 100 feet of fencing to keep her kids safe. The child enclosure will
have the house on one side, so she only needs three sides fenced.
Equation for AREA in standard form:
If the width needs to be 20 feet, what
Sketch your graph:
is the area?
𝐴(𝑤) =
If she wants a total area of 200 ft2,
what should the dimensions be?
What is maximum AREA?
What dimensions will create the
maximum area?
Window 𝑥: [
,
], 𝑦: [
,
]
14) The community fencing in the soccer field. They have 500 feet of fencing to use.
Equation for AREA in standard form:
If the width needs to be 20 feet, what
Sketch your graph:
is the area?
𝐴(𝑤) =
If she wants a total area of 200 ft2,
what should the dimensions be?
What is maximum AREA?
What dimensions will create the
maximum area?
Directions: Given the circle with the given measurements, find the desired lengths or sectors.
̂
15) Length of 𝐾𝐽
16) Area of sector 𝐾𝐽
̂
17) Length of 𝐾𝐼𝐽
18) Argumentative Writing #6.2 (found on last page of your packet!)
Window 𝑥: [
,
], 𝑦: [
,
]
Unit 6 – Understanding Quadratic Functions
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Unit 6 Assignment 5 – Three Forms of Functions (Standard, Vertex, and Factored Forms)
Directions: Given the story problems, identify the key features and answer the questions that follow. USE YOUR OWN PAPER!!!
1) A good football punter will get the ball to hang in the air for as long as possible, thus giving his team a change to
tackle the receiver quickly after a catch. Josh and Billy are both kickers on their football team. Josh kicks with an
initial velocity of 50 feet per second at an initial height of 5 feet. Billy on the other hand, has an initial velocity of 53
feet per second, but an initial height of only 2 feet.
The functions:
Josh’s maximum Value:
Billy’s maximum Value:
Josh: ℎ(𝑡) =
( _____, ______) AND its interpretation: ( _____, ______) AND its interpretation:
Billy: ℎ(𝑡) =
Total hangtime of Josh’s punt:
Total hangtime of Billy’s punt:
When at 1 second, who’s football is higher?
If you were the special team’s coach, who would you
choose to punt for your team? Explain your reasoning.
Directions: MULTIPLE CHOICE PRACTICE. Choose the best answer from the list of possible answers.
2) In circle G, inscribed angle ∠𝐻𝐼𝐽
measures x degrees. Which of
the following describes the
̂?
measure of 𝐻𝐽
a. 2𝑥
b. 𝑥
1
c. 𝑥
3) One parabola shown has an
equation: 𝑦 = (𝑥 − 4)2 + 2.
Which is an equation for the
other?
a) 𝑦 = −(𝑥 − 4)2 + 2
b) 𝑦 = (𝑥 + 4)2 − 2
c) 𝑦 = −(𝑥 − 4)2 − 2
d) 𝑦 = (−𝑥 − 4)2 + 2
2
1
d. 𝑥
4
Directions: Investing in the stock market is always a risk. Sometimes there can be big payouts but other times you can end up losing it all. Use
the information about Maya to set answer the questions that follow.
4) Maya has saved up some money and
decides to take a risk and invest in
some stocks. She invests her money
in Doogle, a popular computer
company. Unfortunately she lost it
all over a matter of months. The
change in her money during this
investment can be represented by:
𝑣(𝑥) = 75 + 72𝑥 − 3𝑥 2 where 𝑣 is
the value of her investment and 𝑥 is
the time in months.
(Graph this function on your calculator)
a. How much money did Maya first
invest in the company?
b. Determine the x-intercepts of the
function.
c. Explain what each x-intercept
means in terms of the problem
situation.
d. Determine the vertex (max/min).
e. Explain what the vertex means in
terms of the problem situation.
f. Determine when her portfolio
reached a value of $360.
5) An artist is building a rectangular stretched canvas to paint an portrait on. He has 14 feet of wood to build the
framing for the canvas.
Diagram:
b) What is the maximum possible area for the portrait?
c) What dimensions will give the maximum area?
Calculator window: x:[
,
] y:[
,
]
a) Write an equation A(w) for the area of the
stretched canvas in terms of the width.
d) For what widths is the area increasing?
e) For what widths is the area decreasing?
CONTINUED ON NEXT PAGE >>>>>>>
Unit 6 – Understanding Quadratic Functions
P a g e | 10
Directions: Write a quadratic function with the given set of characteristics.
6) A parabola that opens downward and has x-intercepts
of (-2,0) and (5,0).
8) A function with maximum value of 9 when 𝑥 = 4
7) A function with vertex at (−1,4) and the parabola
opens up.
9) A function that crosses the 𝑥-axis at -4 and 4.
Directions: (NO CALCULATOR!) Given the function, identify the form of the function as either standard form, factored form, or vertex form. Then state
all you know about the quadratic function’s key characteristics, BASED ONLY ON THE GIVEN EQUATION OF THE FUNCTION!
2
Example:
𝑓(𝑥) = 5(𝑥 − 3)2 + 12
10) 𝑓(𝑥) = 2𝑥 2 − 1
11) 𝑓(𝑥) = 3 (𝑥 + 6)(𝑥 − 1)
The function is in vertex form.
The parabola opens up and
the vertex is at (3,12).
12) 𝑓(𝑥) = (𝑥 + 1)2 − 4
13) 𝑓(𝑥) = −𝑥(𝑥 + 4)
14) 𝑓(𝑥) = (3𝑥 + 2)𝑥
15) 𝑓(𝑥) = −3𝑥 2 + 4𝑥 − 18
Directions: (GRAPHING CALCULATOR) Given the function, use your calculator to find the key features then write all three forms of the function.
16) 𝑓(𝑥) = −2(𝑥 + 4)(𝑥 − 3)
Key Features: Vertex: (___, ___)
Zeros: (___, ___) and (___, ___)
y-intercept (___, ___)
Factored Form:
Vertex Form:
Standard Form:
17) 𝑔(𝑥) = −(𝑥 − 4)2 + 1
Key Features: Vertex: (___, ___)
Zeros: (___, ___) and (___, ___)
y-intercept (___, ___)
Factored Form:
Vertex Form:
Standard Form:
18) ℎ(𝑥) = −3𝑥 2 − 9𝑥 + 12
Key Features: Vertex: (___, ___)
Zeros: (___, ___) and (___, ___)
y-intercept (___, ___)
Factored Form:
Vertex Form:
Standard Form:
Directions: Use your knowledge to set up equations and solve for the variables.
19) A right triangle has a hypotenuse of
14 inches and one angle measures
24°. Find all other sides and angles of
the triangle.
20)
21)
Directions: (GRAPHING CALCULATOR) Given the function, use your calculator to find the key features then write all three forms of the function.
1
22) 𝑓(𝑥) = 2 (𝑥 + 6)(𝑥 + 2)
Key Features: Vertex: (___, ___)
Zeros: (___, ___) and (___, ___)
y-intercept (___, ___)
Factored Form:
Vertex Form:
Standard Form:
23) 𝑔(𝑥) = (𝑥 − 3)2 + 1
Key Features: Vertex: (___, ___)
Zeros: (___, ___) and (___, ___)
y-intercept (___, ___)
Factored Form:
Vertex Form:
Standard Form:
24) ℎ(𝑥) = 5𝑥 2 + 40𝑥 − 45
Key Features: Vertex: (___, ___)
Zeros: (___, ___) and (___, ___)
y-intercept (___, ___)
Factored Form:
Vertex Form:
Standard Form:
Directions: Write a quadratic function in factored form with each set of given characteristics.
25) Write a quadratic function
that represents a parabola
that opens upward and
has x-intercepts (-2,0) and
(5,0).
26) Write a quadratic function
that represents a parabola
that opens downward and
has x-intercepts (2,0) and
(14,0).
27) Write a quadratic function
that represents a parabola
that opens upward and
has x-intercepts (-356, 0)
and (-1,0).
28) Write a quadratic function
that represents a parabola
that opens upward and
has x-intercepts (-112, 0)
and (554, 0)
Unit 6 – Understanding Quadratic Functions
P a g e | 11
Argumentative writing Unit 6 practice #6.2
Problem from Homework:
Write the equation of a
parabola that has a vertex at
(4,3) and a zero at (3,0).
Rex’s equation:
Name __________________________ Period ________
Rex and Slinky are trying to write a quadratic function with the given
information. Look at their equations and decide who is correct. Set up a
logical argument and give evidence to support your claim. BE SURE TO BE
SPECIFIC AND USE FULL SENTENCES!
YOUR CLAIM:
YOUR COUNTERCLAIM:
____________ is correct.
_____________ thought he was correct
because (why could he think he was correct):
Because (your evidence here):
𝑓(𝑥) = (𝑥 − 3)(𝑥 − 5)
But ultimately he is wrong because:
Slinky’s equation:
𝑓(𝑥) = −2(𝑥 − 4)2 + 2
**BE SURE TO HAVE SPECIFIC NUMERICAL
DATA(PROOF) IN YOUR EVIDENCE!**
Argumentative writing Unit 6 practice #6.1
Problem From Homework:
Is the function below linear or
quadratic?
𝑔(𝑥) = 2𝑥 2 + 7 − 2𝑥 2 − 4𝑥
Buzz:
It’s quadratic because the
power is 𝑥 2 and that means it
will be a parabola shape.
Name __________________________ Period ________
Buzz and Woody are doing their math homework together. They
each got a different answer for their latest prompt. Who is correct?
Set up a logical argument and give evidence to support your claim.
BE SURE TO USE FULL SENTENCES!
YOUR CLAIM:
YOUR COUNTERCLAIM:
____________ is correct.
_____________ thought he was correct
because (why could he think she was correct):
Because (your evidence here):
Woody:
It’s linear, because when
I put it in my calculator
and graph it I get this
picture:
But ultimately she is wrong because:
**BE SURE TO HAVE SPECIFIC NUMERICAL
DATA(PROOF) IN YOUR EVIDENCE!**