Unit 4 Quadratic Functions – Part A
 Some mini-quizzes will be unannounced but are always open note.
 HW Assignments will be worth 3 pts. Remember, if you don’t show
work/setup you receive a zero.
 ALL GRAPHS ON GRAPH PAPER
Name____________________________ Period_____
DAY
1
2
3
4
5
6
MINI-QUIZ
B
7
8
9
10
11
12
13
14
15
MINI-QUIZ
C
16
17
18
TOPIC
GRAPHING QUADRATICS FROM VERTEX
FORM
GRAPHING FROM STANDARD FORM AND
IDENTIFYING VERTEX
COMPLETING THE SQUARECHANGING FROM STANDARD TO
VERTEX FORM
ASSIGNMENT
5.1 p. 320… # 1,2,4,5,6,14,15,22-25,39-41
5.2 p. 328… # 1,3-6,14-16, 18, 20, 30, 33A
(try to graph 30 and 33A on your calc)
5.4 p. 345…# 1, 5-7, 14-19
Review day if needed
Mini Quiz
TBA
FACTORING REVIEW
GCF, DIFFERENCE OF SQUARES,
TRINOMIALS
FACTORING REVIEW
PERFECT SQUARE TRINOMIALS AND
MORE TRINOMIALS
ZERO PRODUCT PROPERTY AND
WRITING EQUATIONS WHEN GIVEN THE
ROOTS (ZEROS)
MORE SOLVING BY FACTORING
ZEROS FROM GRAPHING CALCULATOR
AND VERTICAL MOTION PROBLEMS
REVIEW FOR TEST A
TEST A
WORKSHEET A - page 9
SOLVING EQUATIONS BY COMPLETING
THE SQUARE
SIMPLIFYING RADICALS
COMPLEX ROOTS
EQUATING COMPLEX NUMBERS
DISCRIMINANT TEST
QUADRATIC FORMULA
GRAPHING QUADRATIC INEQUALITIESSOLVING QUAD. INEQUALITIES
ADD, SUBTRACT AND MULTIPLY
COMPLEX NUMBERS
POWERS OF I –DIVIDING COMPLEX
NUMBERS
REVIEW
TEST B
WORKSHEET B – page 12
5.3p. 338… # 5-17 (use calc for #11)
5.3 p. 338… # 28-33, 35-59 (odd)
5.3 p. 338…# 18-22, 30-36 (even), 41-43,
46 or 47 (Use your calc to graph)
TBA
Keystone Review
5.4 p. 345 #26-29, 41-45, 48 56, 57
5.5 # p. 353…1, 18-21,26-28, 30,31,34, 37-39,
59-65 (odd)
5.6 p. 361… #1-7, 14-16 (find the discriminant
for 14-16),
WORKSHEET D
5.7 p. 370… # 18-23, 35-45 (odd)
5.9 p. 386 # 12-26
5.9 p. 386…# 27-35, 61-64, 66, 68
WORKSHEET E
Keystone Review
Page 1 of 18
U4 D1: Graphing Quadratics from Vertex Form
1. In unit 2, we looked at transformations  Let’s explore TI Interactive!
Quadratic Equation:
y  a  x  h  k
2
a
h
k
Vertex
2. Examples together: Let’s translate each parabola to find the vertex, then use the “a” value to graph!
a) y   x  2   3
b) y  3  x  1  4
1
c) y   x 2  2
4
Vertex: _______
Vertex: _______
Vertex: _______
2
2
Working backwards: You know the transformation, you have to write the equation.
d) f  x   x2 is stretched vertically by 3 and translated left 2
e) f  x   x2 is reflected across the x-axis and translated 3 units up
Page 2 of 18
The graph below illustrates the area of a room in a newly remodeled house. The “smaller” parabola was the
original size, and the “larger” one represents the new size. Write the function of each parabola as a
transformation of the function f ( x)  x 2 . Next, write the function for the larger size as a transformation of
the function of the original size.
Function of Old Room:
Function of New Room:
Function of Old to New:
Classwork: Mail merge!
Page 3 of 18
U4 D2: Graphing from Standard Form & Identifying the Vertex
1. Yesterday we looked at quadratics in _________________ form. Ex: y  3  x  1  2
2
and the “stretch.”
a. This is convenient because we can easily identify the vertex:
2. However, sometimes quadratics are written in ____________________ form:
3. To review “FOIL,” let’s convert y  3  x  1  2 into standard form.
2
4. From this form, we still want to be able to find the vertex (and other things)…
Standard Form:
Property
y  ax 2  bx  c
Example:
y   x2  2x  2
a positive
a negative
Max or Min?
Vertex
Axis of Symmetry
y-intercept
5. How to graph f ( x)   x 2  2 x  2 …
Step 1: Plot the _________________
Step 2: Sketch the axis of symmetry.
Step 3: Plot the _________________
Step 4: Use symmetry to find __________
Step 5: Sketch!
Page 4 of 18
1) f ( x)  3x 2  2 x  1
2) f ( x)  2 x 2  4 x  2
Direction: _________________
Direction: _________________
Axis of Symmetry: _____________
Axis of Symmetry: _____________
Vertex: _______________
Vertex: _______________
Max or Min (and value): _________& __________
Max or Min (and value): _________& __________
y-intercept: ___________
y-intercept: ___________
WoRd: A record label uses the function a  t   90t 2  8100t to model the sales of a new release. The
number of albums sold is a function of time, t, in days. On which day were the most albums sold? What
is the maximum number of albums sold on that day?
WoRd AGaIn: A r
WoRd
AGaIN
Page 5 of 18
U4 D3: Completing the Square: Change from Standard to Vertex
1. To start class yesterday, we converted the vertex form into standard form…
y   x  3  2
2
2. What if we had to work backwards? y  x 2  10 x  13 .
This is known as ________________________ the square.
y   x 2  10 x  ______   13  ______
Fill the blanks with _______________
Vertex is: _________________
3. One more together: This time there is a number front of x 2 ( a  1 ). Factor it out!!
f ( x)  3x 2  6 x  15
Factor:
Add & Subtract: ___________
Vertex: ________________
Check:
Page 6 of 18
Classwork Problems:
Directions: Fill in the blank for each expression in order to complete the square.
1) x 2  4 x  ______
2) x 2  2 x  ______
3) x 2  8x  ______
Directions: Write each function in vertex form, then identify its vertex.
1)
f ( x)  x 2  6 x  2
6) f ( x)  3x 2  12 x  4
5) f ( x)  x 2  4 x  1
7) f ( x)  2 x 2  16 x  4
Closure:
Vertex form:
Vertex is:
Standard form:
Vertex is:
To complete the square, add and subtract ___________________ to x 2  bx  c .
Page 7 of 18
U4 D4: Factoring Review – GCF, Diff of Squares, Trinomials
Warmup: Following Mini Quiz A – factor the following! Remember, you can FOIL to check!
1) x 2  25
2) 3 x 2  12 x
3) x 2  9 x  14
4) x 2  2 x  48
5) x 2  9
6) 5 x 2  25
1. Factoring is the ____________________ process of expanding (multiplying through the distributive
property, FOIL, etc).
2. Review: Distribute and FOIL
a) 3x  4 x  7 
b)
 x  5 x  6
3. Today we are going to tackle three types of factoring.
2 Terms
3 Terms
GCF
Difference of 2 Squares
Guess and Check
2x  8
4 x 2  49
x 2  11x  30
3x3  15 x 2
a2  4
x 2  x  56
HW Start!
Page 8 of 18
U4 D4: HW – WORKSHEET A
Factor by removing a common factor:
Check by distributing your answer:
1. 5 x 2  10 x 
1.
2. 3 x 2  12 x 
2.
3. 4 x 2  24 
3.
4. 9 x 4  18 x 2 
4.
5. 20 x 2  120 x  240 
Factor using difference of squares,
2
2
a  b  (a  b)(a  b) :
5.
Check by FOILing your answer:
6.
6. x 2  64 
7.
7. x 2  121 
8.
8. 9 x 2  25 
9.
9. x 2  4 y 2 
10.
10. ( x  4)2  9 
Factor:
Check by FOILing your answer:
11. x 2  x  30 
11.
12. x 2  7 x  8 
12.
13. x 2  12 x  20 
13.
14. x 2  6 x  27 
14.
15. x 2  10 x  24 
15.
Factor these various types:
18. x 2  25 
16. x 2  10 x  16 
19. 16 x 2  64 
17. 7 x 3  49 x 
20. 3x 2  6 x  45 
Page 9 of 18
U4 D5: Factoring Review – Perfect Square Trinomials & British
n
1
2
3
4
5
6
7
8
9
10
11
12
13
14
n2
What exponent does a variable have to have in order for it to be a perfect square? ________________!
Perfect Square Trinomials
  x  y   _______________________
2
Examples:

 x  y
2
 _______________________
1) 9 x 2  30 x  25
2) x 2  14 x  49
3) 4 x 2  28 xy  49 y 2
4) 25 x 2  60 x  36
5) x 2  10 x  25
6) 4 x 2  12 x  9
The British Method!
a) 2 x 2  7 x  15
Used when you have ________________________________.
b) 10 x 2  13x  3
Page 10 of 18
Directions: Factor each expression, if possible. If not possible, write “not factorable”
Page 11 of 18
U4 D5: HW – WORKSHEET B
Factor these trinomial squares:
Check by FOILing your answer:
1. x 2  6 x  9 
1.
2. x 2  6 x  9 
2.
3. x 2  16 x  64 
3.
4. x 2  20 x  100 
4.
5. 16 x 2  40 x  25 
6. 9 x 2  6 xy  y 2 
5.
6.
7.
7. 4 x  16 x  16 
2
8. 9 x 2  30 x  25 
9. 16 x 2  48 xy  36 y 2 
8.
9.
10.
10. 25 x 2  70 x  49 
Factor:
Check by FOILing your answer:
11. 2 x 2  13x  15 
11.
12. 3x 2  5 x  2 
12.
13. 4 x 2  12 x  5 
13.
14. 21x 2  58 x  21 
14.
15. 2 x 2  x  6 
16. 6 x 2  10 x  4 
15.
16.
17.
17. 4 x  14 x  6 
2
18.
18. 2 x  11x  12 
2
19. 10 x  13x  3 
19.
2
20.
20. 15 x 2  16 x  15 
Page 12 of 18
U4 D6: Zero Product Property & Writing Eq. when Given Roots
1. Reminder: The graph of a quadratic equation looks like a _______________. Today, we are interested
in finding the place(s) where the graph crosses the ____________________. These values are known as
the ______________________ or the ________________________ of the function (there is a slight
difference, but we don’t need to worry about the technicality).
Today’s Goals:
1) Given the equation, find the roots/zeros/solutions
Zero _______________ Property: If  x  1 x  5  0 , then…
2) Backwards  Given the roots, write the equation
Write as a product and _________________ it out!
2. Examples together: Find the zeros of each function by factoring
a) f ( x)  x 2  x  20
b) g ( x)  2 x 2  9 x  4
3. Examples together: Write a quadratic function in standard form for each given set of zeros.
a) 6 and -3
b) -2 and 7
Classwork Activity (for the rest of today, and tomorrow)!
Page 13 of 18
U4 D8: Zeros from Graphing Calculator and Vertical Motion
1) Yesterday (and probably last year, too!) you learned how to find the zeros of a quadratic function. Today
we are going to look at a real world application of this: _________________ motion
How hard you kick/throw/shoot
the object from the beginning
is 0 (disappears) when…
Example #1: A soccer ball is kicked from the ground level with an initial velocity of 32 ft/s. After how
many seconds will the ball hit the ground?
Step 1: Write the general projectile function

Step 2: Plug in anything you can

Step 3: When does it mean for the ball to hit the ground? Answer: ____________________________!
So, set …
Calculator Notes:
Page 14 of 18
Example #2: Marilyn hit a golf ball on the ground with her driver. Use the general function for a projectile
to write a function that shows the height in feet of her golf ball as a function of time. The ball was hit with
an initial vertical velocity of 100 feet per second.
How long will Marilyn’s ball stay in the air?
Example #3: A rocket is launched from the ground with an initial velocity of 144 ft/sec. (All work is to be
done without using a calculator to graph. You may check your answers by graphing.)
a. Write a function that represents this situation.
b. At what time(s) will the rocket be 320 feet in the air?
c. What is the maximum height of the rocket? How long does it take for the rocket to reach this
height?
d. When will the rocket hit the ground?
Closure: What is the general projectile function? Explain each term. What is the function used for?!
Page 15 of 18
U4 D9: Review for Unit 4 Test A
Directions: Solve by factoring:
1) 3x 2  20  11x
2) x 2  9 x  36  0
3. Use completing the square to put this equation in vertex form. Then find the vertex.
f ( x)  x 2  8 x  3
Vertex form: f ( x)  ___________________________
Vertex:_________________
For the problems below, make sure your answers are in the right format (point, line, number, etc.)!
Find the information below then sketch the graph:
4. f ( x)  ( x  1)2  5
which way does it open?_______________
Has a MAX or MIN?_______________
Vertex: _________________
Axis of Symmetry:_______________
Max / Min value:________________
Use the info to sketch the graph:
Page 16 of 18
5. f ( x)  x 2  6 x  5
which way does it open?_______________
Has a MAX or MIN?_______________
Vertex: _________________
Axis of Symmetry:_______________
Max / Min value:________________
Use the info to sketch the graph:
6. Here’s a graph…tell me the info:
Which way does it open?
Max / Min value:
Has a MAX or MIN?_________
y-intercept:____________
Vertex: _________
x-intercepts:__________
Axis of Symmetry:________
Given that a = -1, write the equation
in vertex form:
__________________________
7. Factor each of the following.
a) 3x3  9 x 2  27 x  6
b) 2 x 2  x  6
_________________________
_____________________________
Page 17 of 18
c) 5 x 2  12 x  4
d) 4 x 2  20 x  25
__________________________
_______________________________
e) 81x 2  16
f) 3x 2  7 x  6
_____________________________
_____________________________
8. For each problem below, you are given the roots of an equation. Find the factors, then write the equation
in standard form.
a) 3 and – 4
b) -17 and –5
________________________
____________________________
9. Use your calculator to find the following information for the quadratic function f ( x)  4 x 2  8 x  5 .
Vertex is________________
zeros are _________________
10. The late great Mr. Rogers dropped a ball in the Land of Make Believe off the top of the castle that has a
height of 50ft.
a) Write a function that describes the position of the ball as a function of time.
b) Determine when the ball hits the ground.
Page 18 of 18