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Name______________________________ Date_______________
Integrated Algebra A Notes/Homework Packet 10
Lesson Homework
Multiplying with Exponents HW #1
Multiplying Monomials HW #2
Distribution & FOIL HW #3
FOIL cont. HW #4
Factoring (GCF) HW #5
GCF cont. HW #6
Difference Between Two Perfect Squares(D2PS) HW #7
Factoring Trinomials HW #8
Factoring Trinomials cont. HW #9
Factoring Trinomials cont. 2 HW #10
Factoring Review HW #11
Graphing Parabolas HW #12
Review
Test
2
Review: Combining Like and Unlike Terms
Give two examples of “like” terms: ___________________
Give two examples of “unlike” terms: ____________________
Like terms have the same _________________ with the same ________________.
Polynomials
A polynomial is named by the number of terms it has.
A monomial has _________ term. Ex: __________________
A binomial has _________ terms. Ex: __________________
A trinomial has _________ terms. Ex: __________________
Combining Like Terms
1. 2x + 5x – 9x = ______________ 2. 22 65 xx = ______________
3. 4x + 5y – 6x + 2y = ______________ 4. x + x + 4a – 5a – x = ________________
5. 32327 xyxy = ______________ 6. xabxab 8452 33 = _______________
7. xxxx 3729 22 = ________________
Multiplying with Exponents
We know that: m2 =
m3 =
So then….. m2 m3 = (m m) (m m m) =
Similarly….. c2 c4 = (c c) (c c c c) =
In general, when x is a number and a and b are positive integers:
xa xb = xa+b
When you multiply numbers with exponents…..
The base remains the same, and then add the exponents.
You must have the same base before you combine the exponents!!!
MULTIPLY – ADD EXPONENTS!!
Example:
x2 x6 = ______________________________ = ____________
54 52 5 = ______________________________ = ____________
3
Practice:
1. x5 x4 = ___________ 5. z3 z4 z5 = ___________
2. x3 x2 = ___________ 6. c c5 = ___________
3. b6 b = ___________ 7. x4 x5 x = ___________
4. m4a m3a = ___________
Dividing with Exponents
x5 x2 can also be written as 2
5
x
x This really means…..
xx
xxxxx
=
In general, when x 0 and a and b are positive integers with a > b:
xa xb = xa – b
When dividing variables with exponents…..
The base remains the same, and then subtract the exponents.
You MUST have the SAME BASE to divide variables with exponents
DIVIDE – SUBTRACT EXPONENTS!!
Simplify the following expressions:
1.x9 x5 = ______ 2. y5 y = ______ 3. c5 c5 = ______
4.3
5
a
a = ______ 5. cy5 cy4 = ______ 6.
a
a
x
x2
5
=______
7.y10b y2b = ______ 8. b
b
a
a = ______
Practice:
1. 26 xx __________ 2. 23 xx ___________ 3. 3yy _________
4. y
y7
__________ 5. 53 xxx __________ 6. 5
5
x
x ____________
4
Name__________________________________ Date________________
HW#1
Combine like terms.
1. 3y + 6x – 6x + y = ______________ 2. 22 216 xx = ______________
3. 5m - 4q + 9 + 2q + 7 = ______________4. 20x2 + 2 + 15x2 - 8 + 3x2 - 4 = _________
5. 6x + 2y + 9 -3x - 5y - 8 = ________________6. x2 + y2 + 8 + 4x2 - 2y2 – 9 = __________
7. x2 + x + x2 + 8x - x = ________________
Simplify the following using the exponent rules:
1. a9 a2 = ______________ 2. a a2 a3 a4 = __________
3. x8 x2 = ___________ 4. k3 k2 = _________
5. k12 k1 = ______________ 6. 9
10
d
d = ____________
7. x7 x3 = ___________ 8. y3 y3 y3 y3 = _________
9. g7m g2m = ______________ 10. h2x h3x h4x = _________
11. x5 x = ___________ 12. a4 a2 = ___________
13. x8 x3 = ______________ 14. d5 d5 d1 = _________
15. x10 x5 = ___________ 16. y5 y2 = ___________
17. d2 d d = ______________ 18. x4 x = ___________
19. x5 x4 = ____________ 20. r2 r4 r5 = _________
21. 2
4
d
d = ____________ 22. x4 x2 x = ______________
Review:
1. What would the equation of the horizontal line be that goes through the point (-4, 1)?
2. Put the following equations into y = mx + b form. (Solve for y).
a. 1532 yx b. xy 35
5
Multiplying Monomials
Procedure:
1. Multiply the coefficients
2. Multiply powers with same base by ________________ EXPONENTS
3. Combine your answers from step 1 and 2
Ex 1: (8x)(3x) _____________ Ex 2: (4x)(8y) ____________
Ex 3: (-4x3y2)(-2xy5) ____________ Ex 4: )2xy)(y5x( 232 (x3) ____________
Practice:
1.(3x)(2x) = _________________ 5.(8d2)(7d5) = _________________
2.(4x2)(3y) = _______________ 6.(10k7)(k4) = __________________
3.(2a4)(5a3) = ______________ 7.(–5hg3)(4h5g5)(-hg) = _________________
4.(5y5)(3y)(2y6) = ______________ 8.(16ab2)(2a2)(-2a4b) = _________________
Dividing Monomials
Procedure:
1. Divide the coefficients
2. Divide powers with same base by ________________ EXPONENTS
(If you get anything to the zero power, it cancels and goes away)
3. Combine your answers from step 1 and 2.
Example 1: Divide 2
5
3a
24a
=_________ Example 2: Divide
32
53
y5x
y20x-
=______
Practice:
1. 2
12
r
r = __________________ 4.
2
23
4
88
xy
yx
= __________________
2. 3
8
c
c = __________________ 5. xt
ytx
42
3 2
= __________________
3. st13
str52 32
= __________________ 6. 11
15
121
11
y
y = __________________
7
Divide the following:
1. 2
18x = __________ 2.
7
14 22
yx = ___________
3. 2
10
6
36
y
y = __________ 4.
x2
x18 2
= ____________
5. 3
32
5
5
y
yx
= __________ 6.
22
34
7
49
bc
bc = _________
7. xy
yx
3
24 2
= __________ 8.
abc
abc
8
56= __________
Review:
1. A triangle has a leg that measures 6m and a hypotenuse that measures 9m.
Determine the length of the other leg.
2. Solve the inequality and graph the solution.
–2y + 8 26
8
Multiplying a Monomial by a Polynomial
(Review of the Distributive Property)
When multiplying polynomials just use the distributive property!! Don’t forget to
combine all like terms in the end.
Let’s Practice:
1. –5(4m – 6n) = 7. –8(4r – 4
1k) =
2. –5c2(15c – 4c2) = 8. 5(d – 3 + d2) =
3. 4(3e – 5) = 9. -3(2x – 1) =
4. 5x(3x – 4) = 10. -2(2x2 – 3x) =
5. 13x3(5x4 – 2x) = 11. 2x(x2 + 3x – 4) =
6. -(3x – 7) = 12. -2x2(4x – x4) =
Multiplying a Binomial by a Binomial
DOUBLE DISTRIBUTING
“F-O-I-L”
We use this expression to describe how to multiply two binomials.
This is VERY similar to the method of DISTRIBUTION.
Example: (x + 3)(x + 6)
F ________ : x x = (multiply the first two terms in the parentheses)
O ________ : x 6 = (multiply the two outer terms)
I ________ : 3 x = (multiply the two inner terms)
L ________ : 3 6 = (multiply the two last terms in the parentheses)
After this is complete, simplify, by combining like terms together to make a
polynomial: x2 + 6x + 3x + 18 = F O I L
9
More Examples:
1. (x + 2)(x + 3) 2. (x – 4)(x – 2)
3. (x2 – 6)(x + 5) 4. (2x + 5)(3x – 4)
Binomials that have the same letters and variables, in the same order, but
different middle signs are called _____________. They are unique, because when
you FOIL them the middle terms cancel each other out.
5. (x + 7)(x – 7) 6. (4x – 3)(4x +3)
Practice:
1. (x + 6)(x + 1) ____________________ = ____________________
2. (x – 5)(x – 3) ____________________ = ____________________
3. (x + 5)(x – 5) ____________________ = ____________________
4. (x2 – 5)(2x – 4) ____________________ = ____________________
5. (5x – 2)(3x – 1) ____________________ = ____________________
6. (2x + 9)(3x2 + 1) ____________________ = ____________________
10
Name__________________________________ Date________________
HW#3
Simplify the following using the distribute property:
1. (8xy)(3xz) = _______________ 2. )2xy)(y5x( 232 = _______________
3. –5(4m – 6n) = _______________ 4. 5c2(15c – 4c2) = _______________
5. m3(6m – 3m4) = _______________ 6. a(a +1) = _______________
7. 5m3(–2 + 3m – 4m2) = ______________ 8. 5(d – 3 + d2) – 10d = _____________
Multiply the following using FOIL. Write your answer in simplest form.
1. (x + 1)(x + 2) = _____________________ 2.(x – 3)(x + 4) = ____________________
3. (x + 3)(x – 4)= _____________________ 4. (x2 – 1)(x + 2)= ___________________
5. (2x – 3)(x + 4)= _____________________ 6. (x + 5)(x – 5)= ___________________
7. (4 – x)(4 + x) = _____________________ 8. (3 – 2x2)(1 + x)= __________________
Review:
1. Simplify : a. 322723 b. 8452
11
FOIL – Day 2
When squaring terms in parentheses you must square the ENTIRE term, which means
that you must write it TWICE!!!
Then use FOIL to complete the problem!
(2x + 3)2 = (2x + 3)(2x + 3) = =
Practice:
1. (a + 3)2 2. (3x – 2)2
3. (y + 2)2 4. (2x – 1)2
Review:
1. (x + 8)(x + 2) 2. (x – 4)(x – 5)
____________________ ____________________
3. (x + 11)(x – 8) 4. (x + 6)(x – 6)
____________________ ____________________
5. (x – 3)(2x – 2) 6. (2x + 13) 2
____________________ ____________________
12
Multiplying a Binomial by a Polynomial
When you multiply a monomial by a polynomial, you use “double distribution.”
Every term in the monomial needs to get multiplied by every term in the
polynomial.
Example 1: (x + 2)(x2 + 2x + 1) Example2: (x +3)(x2 – 6x – 1)
Example 3: (2x – 1)(3x2 +2x + 2) Example 4: (3x – 2)(-x2 +4x – 8)
Practice:
1. )3x3x)(1x( 2 2. )5x7x)(4x( 2
3. )3x4x)(6x( 2 4. )6x9x2)(5x( 2
5. )6x2x)(1x3( 2 6. )3x5x3)(1x4( 2
15
Factoring (Greatest Common Factor)
Greatest Common Factor (GCF) - of two (or more) integers is the largest integer
that is a factor of both (or all) numbers.
Factoring is like ___________________ the ___________________ __________________.
Steps for factoring using a GCF:
1) Find the ______________ ____________ or __________ that can be ______________
out of each term in the polynomial.
2) Place that number ______________ of a set of ______________________.
3) ______________ ____________ ___________ by that number or letter and
__________those ______________in the parentheses separated by + and - signs.
Examples:
1. 2x + 4 = _________ 2. 5y + 25 = ___________ 3. 4a – 16 = ____________
4. ab + ac = __________ 5. xy – xz = ____________ 6. 7ab + 7c = ___________
7. 5c – 30 = ____________ 8. 6x + 8y = ____________ 9. 18x + 24y = ___________
10. 15a + 12b + 6c = ___________________ 11. x3 + x2 + x =____________________
12. 49 yy = ______________________ 13. 35 x3x = ______________________
Practice:
1. x2y + 2y = ___________________ 2. 5x + 15 = ___________________
3. mn – mp = ___________________ 4. 3x – 15c = ___________________
5. 4x – 6y = _____________________ 6. 7h – 7 = _____________________
7. z4y16x10 = ___________________ 8. 46 a3a = ___________________
16
Name__________________________________ Date________________
HW#5
Factor the following using GCF.
1. 3x + 6 = _________ 2. 10y + 30 = ___________ 3. 5a – 15 = ____________
4. cd + ce = __________ 5. gh – gk = ____________ 6. 4ab + 4c = ___________
7. 3c – 30 = ___________ 8. 10a + 8b + 4c = __________ 9. 18p + 9g = ___________
10. 2x3 + 3x2 + 4x = _______________ 11. 121a - 11b = ___________________
12. z3 + 4z2 = _____________ 13. m4 + m7 = __________
Review:
1. Solve the inequality and graph on a number line.
a. 813 x b. 76 x
2. Solve for the x. Round to the nearest tenth.
a. b.
x
10
15
x
7 37
17
Greatest Common Factoring – Day 2
Review: Factor each of the following.
1. 6x – 18 = _______________ 2. 6y + 15z = ______________
3. 2ab + 7a = _____________ 4. 4p – 4 = ________________
When looking for a common factor, you want to find the greatest factor. That
may included more than just a number or letter. It could include a combination
of both.
Example1: 2xa + 2xb = _____________ Example2: 22 x6yx3 = _________________
Example 3: hg8g4 22 = ____________ Example4: x9x6 2 = __________________
Practice: Factor each of the following.
1. 14mn+14mj = __________________ 2. 6xy – 6xz = _____________________
3. 5gh – 15gk = ___________________ 4. xy40yx10 2 = ___________________
5. 22 b8cb24 = ____________________ 6.
2x2y3 5x3y2= __________________
7. 324 ba16ab12 = _________________ 8. x10x6x2 23 = _________________
19
Review:
1. Solve for x. Round to the nearest tenth.
2. Graph the following equation using the slope-intercept method.
2x + y = 6
m = _______ y-int = ________
3. Determine the image and the quadrants of the given points after a
translation.
Image Quadrant
a. (4, 0) T3, –4 _____________ _____________
b. (–1, 1) T2, –1 _____________ _____________
c. (–3, 5) T3, –5 _____________ _____________
d. (–10, 3) T–2, –2 _____________ _____________
e. (8, –2) T3, –4 _____________ _____________
x
40
15cm
20
Only works with 2
terms that are
Perfect Squares and
being Subtracted
Difference Between 2 Perfect Squares
(D2PS)
EVERY PART OF THE EXPRESSION MUST
REPRESENT A PERFECT SQUARE TO USE THIS METHOD
EXAMPLES OF PERFECT SQUARES to Identify
NUMBERS
12
22
32
42
52
62
72
82
92
102
VARIABLES with Even Exponents
x 2
x 4
a6
VARIABLES with Both
x 2
25y4
16b6
Steps:
1. Use two sets of parentheses
1 set of ( ) with a + sign, the other with a – sign
( – ) ( + )
2. Take the square root of both terms.
3. The square root of the first term is placed first in each parenthesis
4. The square root of the second term is placed second in each
parenthesis
Example1:
x2 – 4
Step 1: ( + )( – )
Step 2:
4
x2
Step 3&4: ( + )( – )
Divide even exponent by 2
21
Example2: Example3:
a6 - b2 25 – 16x2
Step 1: ( + )( – ) Step 1: ( + )( – )
Step 2:
2
6
b
a Step 2:
2x16
25
Step 3&4: ( + )( – ) Step 3&4:( + )( – )
Practice:
Factor the following using D2PS.
1. y2 – 1 2. x2 – 64
_______________________ _______________________
3. 1 – 49x2 4. h2 – 16
_______________________ _______________________
5. 100r2 – 9 6. 36 – n2
_______________________ _______________________
7. 144 – 9g2 8. 4g2 – 81h2
_______________________ _______________________
9. 25c2 – 64d2 10. 9x2 – 16
_______________________ _______________________
11. c2 – d10 12. q6 – p6
_______________________ _______________________
22
Name_____________________________ Date_______________
HW #7
Factor the following using D2PS.
1. k2 – 64 2. 81n2 – 100
_______________________ _______________________
3. 25 – r2 4. 36k2 – 49m2
_______________________ _______________________
5. 16n2 – 9 6. 49 – 100k2
_______________________ _______________________
7. n2 – 4m2 8. z2 – y2
_______________________ _______________________
9. 9x6 – 16y14 10. 36 – y2
_______________________ _______________________
Review:
Factor the following using GCF
11. 3x2y + 12xy 12. 12x + 6y
_______________________ _______________________
13. 4k3 – 36k2 14. math – chat
_______________________ _______________________
23
Factoring Trinomials
There are _______ terms in a trinomial,
so we will use a _______ column table to determine the factors of a trinomial.
STEPS: 1. Use two sets of parenthesis
2. Determine the square root of the first term and place it first in each
parenthesis
3. Determine two numbers that multiply to equal the last term
4. Add the factors together to find the coefficient of the middle term
5. Place these two factors second in each parenthesis
Remember factors must:
Multiply to equal the Last term
&
Add to equal the Middle term
If the last term is + (positive)
Both factors will be the same sign
The sign is determined by the sign of the middle term
Ex 1: x2 + 2x + 1
Ex 2: x2 – 10x +9
Ex 3: x2 + 7x + 10 Ex 4: y2 – 8y + 16
_________________________ _________________________
Add to be: ______ LIST
Multiply to be: ______
Add to be: ______ LIST
Multiply to be: ______
_________________________ _________________________
Add to be: ______ LIST
Multiply to be: ______
Add to be: ______ LIST
Multiply to be: ______
24
Ex 5: x2 + 4x + 3 Ex 6: y2 – 5y + 4
***You can check factoring by performing FOIL***
Check Example 5
Practice:
Factor the following using trinomial.
1. m2 + 9m + 18 2. x2 + 10x + 24
_______________________ _______________________
3. x2 – 15x + 36 4. x2 + 5x + 4
_______________________ _______________________
5. d2 – 14d + 48 6. x2 – 9x – 36
_______________________ _______________________
_________________________ _________________________
Add to be: ______ LIST
Multiply to be: ______
Add to be: ______ LIST
Multiply to be: ______
Add to be: ______ LIST
Multiply to be: ______
Add to be: ______ LIST
Multiply to be: ______
Add to be: ______ LIST
Multiply to be: ______
Add to be: ______ LIST
Multiply to be: ______
25
Name_____________________________ Date_______________
HW #8
Factor the following using trinomial.
1. x2 + 6x + 8 2. x2 – 10x + 21
_______________________ _______________________
Check Solution using FOIL Check Solution using FOIL
3. x2 – 13x + 36 4. c2 + 5c + 6
_______________________ _______________________
5. a2 + 6a + 9 6. c2 - 18c + 17
_______________________ _______________________
7. x2 - 8x + 12 8. b2 + 12b + 11
_______________________ _______________________
Review:
Factor the following using D2PS.
9. x2 – 4 10. z2 – 4y2
_______________________ _______________________
11. 4x6 – y14 12. 49 – y2
_______________________ _______________________
13. Simplify 182 14. Simplify 243
26
Factoring Trinomials continued…
Remember factors must:
Multiply to equal the Last term
&
Add to equal the Middle term
If the last term is
(negative)
One factor will be positive One factor will be negative The sign of the middle term determines the location of the larger number
Ex 1: x2 + 2x – 15
Ex 2: x2 – 17x – 18
Ex 3: x2 + 11x – 12 Ex 4: x2 – 9x – 90
Ex 5: x2 + 3x – 10 Ex 6: x2 – 6x – 7
***You can check factoring by performing FOIL***
Check Example 5
Add to be: ______ LIST
Multiply to be: ______
Add to be: ______ LIST
Multiply to be: ______
_________________________ _________________________
Add to be: ______ LIST
Multiply to be: ______
Add to be: ______ LIST
Multiply to be: ______
_________________________ _________________________
Add to be: ______ LIST
Multiply to be: ______
Add to be: ______ LIST
Multiply to be: ______
_________________________ _________________________
27
Practice:
Factor the following using trinomial.
1. b2 + 5b – 24 2. m2 – 4m – 77
_______________________ _______________________
3. x2 + 6x – 27 4. m2 – 6m – 7
_______________________ _______________________
5. c2 + 12c – 28 6. x2 – 3x – 40
_______________________ _______________________
7. y2 + 3y – 18 8. m2 + 13m – 30
_______________________ _______________________
9. a2 + a – 56 10. x2 – 22x – 75
_______________________ _______________________
28
Name_____________________________ Date_______________
HW #9
Factor the following using trinomial.
1. j2 – 2j – 8 2. x2 – 22x – 75
_______________________ _______________________
Check Solution Check Solution
3. a2 + a – 56 4. x2 – 3x – 40
_______________________ _______________________
5. m2 + 13m – 30 6. y2 + 3y – 18
_______________________ _______________________
7. k2 – k – 30 8. x2 – 6x – 16
_______________________ _______________________
Review:
Factor the following using GCF.
9. 16fg+16gh = __________________
10.
3x2y5 4x5y2 = ___________________
11. 22 xy20xy40yx10 =________________
29
Factoring Trinomials (Day 3)
Remember factors must:
________ to equal the _______ term
&
______ to equal the _______ term
Practice Factoring Trinomials
1) x2 + 7x + 12
_______________________
2) x2 – 6x + 8
_______________________
3) x2 + 8x – 20
_______________________
4) x2 – 4x – 21
_______________________
5) x2 – 12x + 27
_______________________
6) x2 + 14x – 32
_______________________
30
Practice:
Factor the following using trinomial.
1. j2 – 2j – 8 2. x2 + 7x + 6
_______________________ _______________________
3. y2 + 5y + 6 4. y2 + 4y - 45
_______________________ _______________________
5. x2 – 15x – 100 6. x2 + 3x + 2
_______________________ _______________________
7. x2 + 6x + 8 8. x2 - 5x - 24
_______________________ _______________________
31
Name__________________________________ Date________________
HW#10
1. a2 – 9a + 20 2. c2 + 12c – 28
_______________________ _______________________
3. y2 + 3y – 18 4. m2 + 13m – 30
_______________________ _______________________
5. x2 – 15x + 36 6. x2 – 22x – 75
_______________________ _______________________
7. a2 + a – 56 8. x2 – 3x – 40
_______________________ _______________________
9. x2 – 13x + 36 10. k2 – k – 30
_______________________ _______________________
32
Factoring Review
(GCF, D2PS, Trinomial)
Determine what type of factoring each problem is (GCF, D2PS, or Trinomial) and
then factor it.
1. x3 + x2 2. 8x + 2y
_______________________ _______________________
3. x2 – 13x + 36 4. 121 – x2y2
_______________________ _______________________
5. ab + ac + ab + ac 6. x2 + 11x + 24
_______________________ _______________________
7. x2 – 49 8. x2 – 10x + 21
_______________________ _______________________
33
9. x2 – y2z4 10. x2y – 10xy2
_______________________ _______________________
11. 5x2 – 10xy2 12. y2 + 14y + 45
_______________________ _______________________
13. 25x2 – 36y2 14. y2 + 3y - 40
_______________________ _______________________
34
Name__________________________________ Date________________
HW#11
Factor the following expressions. You must decide whether to use GCF, D2PS or
trinomials.
1. x2 – 13x + 36 2. 3c – 30
_______________________ _______________________
3. k2 – k – 30 4. x2 – 49
_______________________ _______________________
5. 3x + 6 6. 10y + 30
_______________________ _______________________
7. a2 + a – 56 8. x2 – y2z4
_______________________ _______________________
9. cd + ce 10. x2 – 3x – 40
_______________________ _______________________
11. 25x3 – 5x2 12. 5a – 15
_______________________ _______________________
13. 16p2 - 9 14. x2 + 12x + 27
_______________________ _______________________
15. a6 - 4c2 16. 10a + 8b + 4c
_______________________ _______________________
35
Parabolas
The Quadratic Equation is written as: _______________________.
The graph of this equation is called a __________________.
Let’s sketch what a parabola looks like.
We are going to label some of the parts of a parabola.
A parabola can open up (smile) or down (frown). We know this by our
coefficient in front of the x2 term.
If it is positive coefficient, the parabola will open _________ (or __________).
o The turning point will be a ______________.
If it is negative coefficient, the parabola will open ________ ( or _________).
o The turning point will be a ______________.
Let’s decide if the following will open up or down and if their turning point is a
maximum or minimum just by looking at their equations:
OPENS (up or down) TURNING POINT (max or min)
1. y = x2 + 2 __________ _______________
2. y = x2 + 3x + 2 __________ _______________
3. y = -x2 + 4 __________ _______________
4. y = x2 – 8x + 7 __________ _______________
5. y = 3x2 – 4x + 1 __________ _______________
6. y = –x2 + 2 __________ _______________
7. y = x2 – 4x – 3 __________ _______________
8. y = –x2 – 2 __________ _______________
9. y = -2x2 – 6x – 8 __________ _______________
10. y = x2 – 2x __________ _______________
y
x
Word Bank:
Turning Point
Axis of
Symmetry
Roots
36
We can graph parabolas using our calculator.
STEPS:
Enter the equation into y =
Go to the table, Find the turning point and copy down
the xy-table with 3 points above the turning point and 3 points below the
turning point.
Graph the points and label the graph.
Example 1: GRAPH: y = x2 – 8x + 7
Example 2: GRAPH: 3xy 2
Example 3: GRAPH: y = –x2 – 4x – 3
2nd GRAPH
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Name__________________________________ Date________________
HW#12
Determine if the following will open up or down and if their turning point is a
maximum or minimum.
OPENS TURNING POINT
1. y = -x2 + 4 __________ _______________
2. y = x2 + 2x -1 __________ _______________
3. y = -3x2 + 4 __________ _______________
4. y = 2x2 + 5x + 1 __________ _______________
5. y = 4x2 – 4x __________ _______________
6. y = –3x2 - 6 __________ _______________
7. y = x2 – 4x – 3 __________ _______________
8. y = 3x2 – 2 __________ _______________
9. y = -5x2 +10x __________ _______________
10. y = -x2 – 2 __________ _______________
Graph the following parabolas:
1. y = x2 – 2x 2. y = 2x2 - 4x + 1