Minds On: Turn & Talk Which of these are QUADRATIC EQUATIONS? y = x 2 y = 3x 3 – 2x 2 + 1 y = 4x 2...
-
Upload
dwayne-strickland -
Category
Documents
-
view
223 -
download
0
Transcript of Minds On: Turn & Talk Which of these are QUADRATIC EQUATIONS? y = x 2 y = 3x 3 – 2x 2 + 1 y = 4x 2...
Minds On: Turn & Talk
• Which of these are QUADRATIC EQUATIONS?
y = x2 y = 3x3 – 2x2 + 1 y = 4x2 + 2x – 5 x2 + y2 = 64- 7x2 + y + 3 = 0 y = 4x + 5
Quadratic Not Quadratic
A quadratic equation is a “second order” or “second degree” equation, meaning the variable x has an exponent of 2 (but not higher than 2) and y always has an exponent of 1.
Lesson 1: Expanding
Learning Goal:
I can turn factored form quadratic equations into standard form by expanding (FOIL) and simplifying
MFM 2P – Unit 4: Algebra
Skills Reminder! “Collecting Like Terms”a) b)
Lesson 1: ExpandingMFM 2P – Unit 4: Algebra
a(b + c)
Dog pees EVERYWHERE
Lesson 1: ExpandingMFM 2P – Unit 4: Algebra
Recall: Distributive Property
a) 3(x – 7)
b) -(-2a + b – 3ab)
c) -4(3x2 – 2x + 4y)
Lesson 1: ExpandingMFM 2P – Unit 4: Algebra
Recall: Distributive Property
Lesson 1: ExpandingMFM 2P – Unit 4: Algebra
Expanding means to multiply. Up until now we have multiplied a monomial by a binomial.
4( 5x – 8)
Now we will multiply a binomial by a binomial.
(x + 2)(x – 8)
• There are THREE different forms of the QUADRATIC EQUATION
• Each is uniquely useful
Standard Form Factored Form Vertex Formy = ax2 + bx + c y = a(x – s)(x – t) y = a(x – h)2 + k
Lesson 1: ExpandingMFM 2P – Unit 4: Algebra
• There are THREE different forms of the QUADRATIC EQUATION
Standard Form Factored Form Vertex Formy = ax2 + bx + c y = a(x – s)(x – t) y = a(x – h)2 + k
Y-in
terc
ept
X-in
terc
ept
(“ze
ro”)
X-in
terc
ept
(“ze
ro”)
X-va
lue
of
verte
xy-
valu
e of
ve
rtex
Lesson 1: ExpandingMFM 2P – Unit 4: Algebra
• What happens when a is NEGATIVE?
Standard Form Factored Form Vertex Formy = ax2 + bx + c y = a(x – s)(x – t) y = a(x – h)2 + k
Lesson 1: ExpandingMFM 2P – Unit 4: Algebra
Moving between Factored and Standard Forms
Factored Formlike
y = (x + 2)(x + 4)
Standard Formlike
y = x2 + 6x + 8
EXPAND
FACTOR
Lesson 1: ExpandingMFM 2P – Unit 4: Algebra
If I gave you this equation: y = x2 – x - 6
and asked you to graph it, what would you do?
Lesson 1: ExpandingMFM 2P – Unit 4: Algebra
-10 -8 -6 -4 -2 2 4 6 8 10
-10
-8
-6
-4
-2
2
4
6
8
10
x
y
If I gave you this equation: y = (x -3)(x +2)
and asked you to graph it, what would you do?
Lesson 1: ExpandingMFM 2P – Unit 4: Algebra
-10 -8 -6 -4 -2 2 4 6 8 10
-10
-8
-6
-4
-2
2
4
6
8
10
x
y
• In order to graph a parabola, we need both the standard form and the
factored form equations.
If we are only given 1 of these equations, we need to change it into the other form so that we have both
forms.
Lesson 1: ExpandingMFM 2P – Unit 4: Algebra
Lesson 1: ExpandingMFM 2P – Unit 4: Algebra
We can use the chart method to expand.
Lesson 1: ExpandingMFM 2P – Unit 4: Algebra
Lesson 1: ExpandingMFM 2P – Unit 4: Algebra
We can also use the chart method when we need to multiply 2 binomials (or in other words: change a factored form equation into standard form).
Lesson 1: ExpandingMFM 2P – Unit 4: Algebra
Lesson 1: ExpandingMFM 2P – Unit 4: Algebra
(x + a)(x + b)
MULTIPLE Dogs pee
EVERYWHERE
Lesson 1: ExpandingMFM 2P – Unit 4: Algebra
Remember the Dog Pee method? We can use that to multiply two binomials as well!
a) (x + 4)(x – 3)
b) (3x + 5)(x – 1)
Lesson 1: ExpandingMFM 2P – Unit 4: Algebra
We call this method FOIL
F – FirstO – OutsideI – InsideL – Last
Lesson 1: ExpandingMFM 2P – Unit 4: Algebra
Lesson 1: ExpandingMFM 2P – Unit 4: Algebra
Outside
Inside
Last
First
Lesson 1: ExpandingMFM 2P – Unit 4: Algebra
Lesson 1: ExpandingMFM 2P – Unit 4: Algebra
Lesson 1: ExpandingMFM 2P – Unit 4: Algebra
y = (x – 2)2
Consolidation:
• Why do we FOIL?
Lesson 1: ExpandingMFM 2P – Unit 4: Algebra
Remember:• There are THREE different forms of the
QUADRATIC EQUATION
• Each is uniquely useful
Standard Form Factored Form Vertex Formy = ax2 + bx + c y = a(x – s)(x – t) y = a(x – h)2 + k
MFM 2P – Unit 4: Algebra
Lesson 1: Expanding
Learning Goals revisited
• I can turn factored form quadratic equations into standard form by expanding (FOIL) and simplifying