# Quadratics

### Algebra

## 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)