Quadratic Relations

Expanding, Factoring, Solving, & Completing the Square

PART I: Expanding

Expanding is simple as long as you follow the rules of BEDMAS (Brackets, Exponents, Division/Multiplication, and Addition/Subtraction).


When expanding, you need to make sure that you always "break" or "open" the brackets.


To do so you must always take note that there is always a number outside the bracket. This number must be multiplied to every term in the bracket.

PART II: Factoring

Common Factoring

Factoring is the opposite of expanding. If every term of a polynomial is divisible by the same constant, it is called a common factor. To completely factor a polynomial, you must factor out the Greatest Common Factor (GCF).

Factoring By Grouping

Factoring by grouping is used when the terms in a polynomial do not share a common factor.

Factoring by Simple Trinomials (Product and Sum)

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Factoring Complex Trinomials (Decomposition)

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Factoring by Difference of Squares

Whenever you see a perfect square that is negative, there's always a possibility that it can be factored by squares.

PART III: Solving Quadratic Relations (Solving for "X")

There are 3 ways to solve for "x". One method would be to factor the equation and solve for the "x" while the second method would be to plug the equation into the quadratic formula. A quadratic equation can consist of a maximum of two x-intercepts (roots) or a minimum of no x-intercepts (roots). The last method, would be by graphing however, the other two methods stated before would be much more efficient.

PART IV: COMPLETING THE SQUARE

What is "Completing the Square"?

Completing the square is the process of turning a standard equation into vertex form. To do so you must follow 6 simple steps.

BY: Nela Ratnam - Mr. Ly Period 4