Quadratic expressions

Question 1

The 2 signal for Quads…

Answer 1

An expression with a squared variable

Set up for a squared product like (x-3)(x+4)

Question 2

Roots are what? and how many exist

Answer 2

Roots are the solutions to a quad, typically there are two but sometimes only 1 exists

Question 3

How to distribute two expressions…

Answer 3

use FOIL, every term gets multiplied following this order

Question 4

Opposite of distributing is… and how do I solve?

Answer 4

factoring. Consider relationship of coefficient on the variable term and the constant at the end.
- The coefficient is the SUM of the factored pair
- The constant is the product of the same pair

Question 5

Zero product rule? and why it matters

Answer 5

Set quad to zero before proceeding… you can then find out the potential roots for a variable

Question 6

If every term in expression is multiplied by a common number or the squared term is negative… what can I do?

Answer 6

Factor out that number. If the squared term is negative simply factor out -1

Question 7

Never create ___ when dividing a number off the squared term.

Answer 7

a Fraction term!

Question 8

A quad with NO coefficient term.

Exp X^2 - 9

Answer 8

Take square roots of the constant and record both negative/positive possibilities.

Watch out: if the result under the square root is negative, the solution is imaginary

Question 9

A quad with NO constant

X^2 - 2x

Answer 9

Simply factor out the variable

X (x - 2)

Question 10

Quads with higher powers can be solved by? Also what does the largest power tell you??

X^3 - 3x^2 + 2x

Answer 10

Factor X to the front! The largest power reveals the number of roots, if problem said X does not equal 0, you can ignore

X (x^2 - 3x +2)

Question 11

How to approach quads in fractions??

Answer 11

Same process except first you must cancel out common factors…

Can multiply each term by an LCM

OR

factor out a term in the numerator and then cancel out with denominator