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Unit 1A: Quadratics Revisited
2017
pebblebrook high schoolALGBRA 2
1.1 – 1.8
1.1 Multiplying Binomials
Example 1Multiply: (x +2)(x +4)
Example 2Multiply: (2x +3)(5x + 8)
You Try……
Think-Write-Discuss
Section 1.1 Homework
1.2 Factoring Quadratics: GCF
_______________________ is rewriting an expression the _________________ of its factors.
The ______________ is the common factor with the greatest __________________ and the greatest __________________.
Example 1: Identify the GCF1)4x2, 20x, 12 2) 9n2, 24n
Steps to factor a quadratic expression:
Identify the GCF Divide EVERY term by the GCF Rewrite using the Distributive
Property
Example 2: Factoring using GCF1) 9x2 + 3x – 18 2) 7p2 + 21
3) 4w2 + 2w
You Try….1) 3a2 – 9a 2) 25b2 – 35b + 5
CHALLENGE: Factor: 8x3y2 – 4xy
Section 1.2 HomeworkFactor the GCF
1.3 Factoring Quadratics: a = 1A ____________________ is an expression in the form ax2 + bx + c.
You can factor many quadratic trinomials into _____ __________ _____________.
Example: Factor
1) x2 + 8x + 7
2) x2 -17x + 72
3) x2 – x -12
4) x2 - 9
You Try....1) x2 + 12x + 32
2) x2 – 11x + 24
3) x2 + 3x – 10
4) x2 - 144
Section 1.3 Homework
1.4 Factoring Quadratics: a ≠ 1 & GCFFactoring completely implies factoring out the GCF
1 st , then factor as a product of 2 binomials.
Steps for factoring completely:
Identify the GCF Divide EVERY term by the GCF Rewrite using the Distributive
Property Factor the remaining trinomial using
AC-Method
Examples: Factor completely
1) 2x2 + 6x + 4
2) 3x2 – 39x + 36
3) 2x2 – 10x – 28
4) 3x2 - 12
You Try…..
1) 3x2 + 12x – 15 2) 9x2 - 36
Sometimes you don’t have a GCF. Examples: Factor completely.
1) 2x2 + 7x – 9
2) 3x2 – 16x -12
3) 4x2 + 5x - 6
You Try…..
1) 3x2 + 7x – 20
2) 2x2 – 19x + 24
Section 1.4 Homework
1.5 Solving Quadratics: Factoring
“Solving” a quadratic implies finding the __________ that make the equation equal to zero.
This is sometimes referred to _________ of the
function.
Finding zeros by factoring… Write equation in standard form; equal to zero.
Factor the trinomial. Set each binomial equal to zero.
Solve each binomial for x.
Examples: Solve by factoring
1) 2x2 – 11x = -15
2) 2x2 + 4x = 6
3) x2 + 6x + 8 = 0
4) 3x2 – 5x – 4 = 0
You Try …..
1)16x2 = 8x
2) x2 + 7x = 18
3) 2x2 – x – 3 = 0
Section 1.5 Homework
1.6 Solving Quadratics: Square Roots
This method is best used when the linear term is missing.
ax2 + c = 0
Examples:
1) 5x2 – 180 = 0
2) 4x2 – 25 = 0
3) 3x2 = 24
4) x2 = 14
You Try….1) 5x2 = 80
2) x2 = 4
3) 3x2 = 15
Section 1.6 Homework
1.7 Solving Quadratics: Quadratic Formula
(Real Solutions)
What happens when you can’t factor? Use the Quadratic Formula!
Examples: 1) 2x2 + 6x + 1 = 0
2) 3x2 – 5x = -2
You Try…
1) x2 – x – 1 =0
2) x2 + 4x = 41
Section 1.7 Homework
1.8 Discriminant
NO SOLUTION MEANS COMPLEX SOLUTION.
Example 1: Tell the type & number of solutions
1) x2 + 6x + 8 = 0
2) x2 – 4x – 5 = 0
3) 2x2 + 7x – 15 = 0
You Try…1) x2 + 6x + 10 = 0
2) 6x2 – 2x + 5 = 0
Section 1.8 Homework