QUADRATICS

Question 1

What is a Quadratic Equation

Answer 1

An equation that employs the variable x having the general form ax^2 + bx + c = 0, where a, b, and c are constants and a does not equal zero; that is, the variable is squared but raised to no higher power.

Usually a two solution problem.

The constant a often presents as a 1 and so is invisible and the equation can look like x2 + bx + c = 0

Question 2

How to Solve Quadratic Equations Using FOIL

Answer 2

1. Move everything to one side so the equation equals Zero —>
   x^2 + 3x + 8 = 12 –> x^2 + 3x - 4 = 0
2. Reverse FOIL / Factor Out the equation
   x^2 + 3x - 4 = 0 —> (x+4) (x-1) = 0
3. Recognize that (x+4) or (x-1) must equal zero, so X is either -4 or 1

Question 3

What is FOIL?

Answer 3

We use FOIL to take a binomial pair in a parentheses and turn it into a quadratic —> (2x + 3) (5x - 8)

F: First —> Multiply the first coefficients together
O: Outer —> Multiply the outer coefficients together
I: Inner —-> Multiply the inner coefficients together
L: Last —–> Multiply the last coefficients together

Question 4

How to Reverse FOIL?

Answer 4

What if I have a quadratic and need to turn it into a pair to solve it?

You reverse the foiling to the factored form! How!?

ax^2 + bx + c = 0 —>

1. ax^2 is easy it’s becoming ax again
2. the factored form will require two numbers that added equal the constant of b and multiplied equal the constant of c. Find those and you’ve reverse foiled!
3. Remember to keep the signs of numbers in mind as a neg x a neg = positive and etc

Question 5

Special Product 2: x^2 + 2xy + y^2 = ?

Answer 5

A common form of a quadratic whose reverse foiled form results in: x^2 + 2xy + y^2 = (x+y)^2

Question 6

Special Product 3: x^2 - 2xy + y^2 = ?

Answer 6

A common form of a quadratic whose reverse foiled form results in: x^2 - 2xy + y^2 = (x-y)^2

Question 7

What are the common ways a quadratic is disguised within an equation?

Answer 7

1. It is hidden within another equation out of which a variable must be factored out to reveal the quadratic.
2. It is spread on two sides of an equal side and must be rebalanced to reveal the quadratic.

Question 8

When do Quadratics only have one solution?

Answer 8

When c = b^2 / 4

Question 9

Special Product 1: x^2 - y^2 = ?

Answer 9

A common form of a quadratic whose reverse foiled form results in: x^2 - y^2 = (x+y) (x-y)