Quadratics

Algebra

Unit 4 Outline

Solving Quadratic Equations by Factoring (Common Factoring, Multiplying Binomials and Factoring Simple Trinomials)

Complex Trinomials (Decomposition)

Solving Quadratic Equations by Using a Formula

Solving by Completing the Square

Expanding and Simplifying

Vocabulary

Binomial: An algebraic expression that consists of two terms. for example, 4x-7y

Completing the Square: Adding a constant number to a quadratic expression to form a perfect square

Difference of Squares: A way of factoring applied to an expression that can be expressed as (a + b)(a - b)

Factored Form of a Quadratic Relation: a quadratic relations in the form y= a(x-s)(x-t) which shows that the zeros of this relation are s and t

Quadratic Formula: the formula that determines the roots of a quadratic equation

Review Questions

Factoring

Factor out the common factors(if any):

a)7x-14

b) 10-15x

c) 12x+8

d) 24x^2 + 36x -12

e) 18x-12x^2


Trinomial Factoring:

a) 2x^2 + 5x + 3

b) 2x^2-x-10

c) 4x^2 + 27x +18

d) 15x^2 +14xy -8y^2


Difference of Squares:

a) x^2-16

b) x^2 - 81

c) 9x^2 - 25

d) 100-x^2y^2


Simple Trinomials:

a) x^2 + 10x + 24

b) c^2 -17c + 72

c) x^2 -2x - 4

d) x^2 + 8x - 48


Factor Completely:

a) (2x-3)^3 - (3x +2)^3

b) 8x^4 - x

c) 16(x +1)^3 + 2

d) 7a^3 + 56b^3


Combinations (choose the most APPROPRIATE method!)

a) y-x^2y

b) 2x^2-8x-42

c) 18x^3-21x^2+6x

d) 36x^3y-100xy


Decomposition:

a) 9x^2 + 48x + 64

b)x^2 + 50x + 49

c) 4x^2 + 65x + 16

d) x^2 - 34x -111

e) 2x^2 + 11x + 5

Solving Quadratic Equations by Factoring - MathHelp.com

Quadratic Formula

Solve By Using the Quadratic Formula

Often, the simplest way to solve ax^2 + bx + c = 0 to find the value of X is to factor the quadratic, set each factor equal to 0 and then solve each factor. But sometimes factoring may get to messy or you might not be able to factor at all, and when factoring doesn't work the quadratic formula can always find the solution.


Solve the following by using the quadratic formula:
a) x^2 + 3x - 4 = 0

b) 2x^2 - 4x - 3 = 0

c) 6x^2 + 11x - 35 = 0

d) 3x^2 + 6x + 10 = 0

Algebra Help - The Quadratic Formula - MathHelp.com

Completing the Square

By completing the square, you have to rearrange the quadratic into the neat (squared part) equals (a number) form to solve by completing the square.


Solve by Completing the Square:


a) x^2 - 8x + 5 = 0

b) 3x^2 - 12x - 7 = 0

c) 4x^2 + 8x - 9 = 0

d) 5x^2 + 20x + 32 = 0

e) -3x^2 - 18x - 35 = 0

f) x^2 + 12x + 4 = 0

g) -2x^2 -12x -9 = 0

h) -x^2 -2x -5 = 0

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Completing The Square - MathHelp.com - Algebra Help

Expanding and Simplifying

Expand and simplify the following, if possible:

a) (2x + 5)^2

b)(2x-1)((x+3)

c) (4x -1) (x + 2)

d) (6x + 3)^2

e) (2x + 8)^2

f) (x + 3)^2 (x-1)