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
Quadratic Formula
Solve By Using the Quadratic Formula
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
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
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)