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