1. Minds On: Turn & Talk y = x2 y = 3x3 – 2x2 + 1 y = 4x2 + 2x – 5
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.
2D Currie 2013 Quadratics Part 1

2. Lesson 1: Expanding Learning Goal:
MFM 2P – Unit 4: Algebra
Lesson 1: Expanding
Learning Goal:
I can turn factored form quadratic equations into standard form by expanding (FOIL) and simplifying
2D Currie 2013 Quadratics Part 1

3. Skills Reminder! “Collecting Like Terms”
MFM 2P – Unit 4: Algebra
Lesson 1: Expanding
Skills Reminder! “Collecting Like Terms” b)
On the handout.
2D Currie 2013 Quadratics Part 1

4. a(b + c) Lesson 1: Expanding Dog pees EVERYWHERE
MFM 2P – Unit 4: Algebra
Lesson 1: Expanding
Recall: Distributive Property
a(b + c)
Dog pees EVERYWHERE
2D Currie 2013 Quadratics Part 1

5. Lesson 1: Expanding 3(x – 7) b) -(-2a + b – 3ab) c) -4(3x2 – 2x + 4y)
MFM 2P – Unit 4: Algebra
Lesson 1: Expanding
Recall: Distributive Property
3(x – 7)
b) -(-2a + b – 3ab)
c) -4(3x2 – 2x + 4y)
After these examples, Now you try c) and d) on the handout.
2D Currie 2013 Quadratics Part 1

6. 4( 5x – 8) (x + 2)(x – 8) Lesson 1: Expanding
MFM 2P – Unit 4: Algebra
Lesson 1: Expanding
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)
Ask students what the second example (binomial by a binomial) looks like? FACTORED FORM
2D Currie 2013 Quadratics Part 1

7. Lesson 1: Expanding Standard Form Factored Form Vertex Form
MFM 2P – Unit 4: Algebra
Lesson 1: Expanding
There are THREE different forms of the QUADRATIC EQUATION
Each is uniquely useful
Standard Form
Factored Form
Vertex Form
y = ax2 + bx + c
y = a(x – s)(x – t)
y = a(x – h)2 + k
Students view “Comparing Quadratic Equations and Graphs” worksheet. They will each need several colours of highlighters.
2D Currie 2013 Quadratics Part 1

8. Lesson 1: Expanding Standard Form Factored Form Vertex Form
MFM 2P – Unit 4: Algebra
Lesson 1: Expanding
There are THREE different forms of the QUADRATIC EQUATION
Standard Form
Factored Form
Vertex Form
y = ax2 + bx + c
y = a(x – s)(x – t)
y = a(x – h)2 + k
X-intercept (“zero”)
X-value of vertex
X-intercept (“zero”)
y-value of vertex
Y-intercept
Stars denote the need to FLIP THE SIGN from what they see in the equation in order to make the transition to the graph.
SO we need ways to get from one form to the other.
2D Currie 2013 Quadratics Part 1

9. Lesson 1: Expanding What happens when a is NEGATIVE? Standard Form
MFM 2P – Unit 4: Algebra
Lesson 1: Expanding
What happens when a is NEGATIVE?
Standard Form
Factored Form
Vertex Form
y = ax2 + bx + c
y = a(x – s)(x – t)
y = a(x – h)2 + k
2D Currie 2013 Quadratics Part 1

10. Moving between Factored and Standard Forms
MFM 2P – Unit 4: Algebra
Lesson 1: Expanding
Moving between Factored and Standard Forms
EXPAND
Factored Form
like
y = (x + 2)(x + 4)
Standard Form
like
y = x2 + 6x + 8
Why do we need to be able to go from one form to another?
FACTOR
2D Currie 2013 Quadratics Part 1

11. MFM 2P – Unit 4: Algebra
Lesson 1: Expanding
If I gave you this equation: y = x2 – x - 6 and asked you to graph it, what would you do?
Why do we need to be able to go from one form to another?
2D Currie 2013 Quadratics Part 1

12. MFM 2P – Unit 4: Algebra
Lesson 1: Expanding
If I gave you this equation: y = (x -3)(x +2) and asked you to graph it, what would you do?
Why do we need to be able to go from one form to another?
2D Currie 2013 Quadratics Part 1

13. MFM 2P – Unit 4: Algebra
Lesson 1: Expanding
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.
Why do we need to be able to go from one form to another?
2D Currie 2013 Quadratics Part 1

14. Lesson 1: Expanding We can use the chart method to expand.
MFM 2P – Unit 4: Algebra
Lesson 1: Expanding
We can use the chart method to expand.
These are on the handout now.
One together,
One on your own.

15. Lesson 1: Expanding MFM 2P – Unit 4: Algebra
These are on the handout now.
One together,
One on your own.

16. MFM 2P – Unit 4: Algebra
Lesson 1: Expanding
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).
These are on the handout now.
One together,
One on your own.
Now finish the rest of the in-class handout.

17. Lesson 1: Expanding MFM 2P – Unit 4: Algebra
These are on the handout now.
One together,
One on your own.
Now finish the rest of the in-class handout.

18. Lesson 1: Expanding MFM 2P – Unit 4: Algebra
Invite students to come up and record their answers.
Emphasize need to write out and simplify (not just fill in the boxes).

19. MULTIPLE Dogs pee EVERYWHERE
MFM 2P – Unit 4: Algebra
Lesson 1: Expanding
Remember the Dog Pee method? We can use that to multiply two binomials as well!
(x + a)(x + b)
MULTIPLE Dogs pee EVERYWHERE
2D Currie 2013 Quadratics Part 1

20. Lesson 1: Expanding (x + 4)(x – 3) b) (3x + 5)(x – 1)
MFM 2P – Unit 4: Algebra
Lesson 1: Expanding
(x + 4)(x – 3)
b) (3x + 5)(x – 1)
2D Currie 2013 Quadratics Part 1

21. F – First O – Outside I – Inside L – Last We call this method FOIL
MFM 2P – Unit 4: Algebra
Lesson 1: Expanding
We call this method FOIL
F – First
O – Outside
I – Inside
L – Last
2D Currie 2013 Quadratics Part 1

22. Lesson 1: Expanding Outside First Inside Last MFM 2P – Unit 4: Algebra
Inside
Last
2D Currie 2013 Quadratics Part 1

23. MFM 2P – Unit 4: Algebra
Lesson 1: Expanding

24. MFM 2P – Unit 4: Algebra
Lesson 1: Expanding

25. MFM 2P – Unit 4: Algebra
Lesson 1: Expanding
y = (x – 2)2

26. Lesson 1: Expanding Consolidation: Why do we FOIL?
MFM 2P – Unit 4: Algebra
Lesson 1: Expanding
Consolidation:
Why do we FOIL?
To turn a factored quadratic equation into a standard form one
2D Currie 2013 Quadratics Part 1

27. Lesson 1: Expanding Standard Form Factored Form Vertex Form Remember:
MFM 2P – Unit 4: Algebra
Lesson 1: Expanding
Remember:
There are THREE different forms of the QUADRATIC EQUATION
Each is uniquely useful
Standard Form
Factored Form
Vertex Form
y = ax2 + bx + c
y = a(x – s)(x – t)
y = a(x – h)2 + k
So remember this is WHY we FOIL – to get from factored form to standard form.
2D Currie 2013 Quadratics Part 1

28. Learning Goals revisited
I can turn factored form quadratic equations into standard form by expanding (FOIL) and simplifying
2D Currie 2013 Quadratics Part 1