## Freeman Chapter 13

by Pixi O'Reilly
## 1. 13.1

### 1.1. Square Root Property

1.1.1. 1. Solve polynomials 2. When removing square root, use plus or minus 3. Finish solving with plus or minus answers

### 1.2. Completing the Square

1.2.1. 1. Find third term (1/2 of coefficient squared) = ( 1/2 (x) )^2 2.Do both to both sides 3. Simplify 4. Solve with square root property 5.Get x by itself

## 2. 13.2

### 2.1. Quadratics

2.1.1. Formula

2.1.1.1. ax^2 +bx+c=0 Opposite of b, times the square root of, b squared minus four times a times c, divided by two times a

2.1.1.2. 1. Multiply by LCD to rid fractions 2. Plug directly into Quadratic formula 3. Solve for x 4. Check to factor out of radical

2.1.2. Discriminant (Inside radical)

2.1.2.1. 2 rational - perfect squares 2 irrational - radicals 2 complex - negative numbers 1 rational number - equal to 0

2.1.3. Creating equalities from solutions

2.1.3.1. 1. Set to x = 2. Set to zero (get everything on one side) 3. Set to factored ( )( )=0 -rid fractions with LCD 4. FOIL 5. Standard form - variables on one side of =, numbers on the other

## 3. 13.3

### 3.1. Graphing Parabolas

3.1.1. 1. Find vertex - y=a(x-h)^2+k then v=(h,k) or -b/2a and plug in 2. Min/max - a = + min or a = - max 3. Decide x intercepts, let y=0, solve for x -factor -quad form 4. Y intercepts, let x=0, solve for y 5. Axis of symmetry is min/max vertical line 6. Domain = X (all real numbers) 7. Range = Y

## 4. 13.5

### 4.1. Polynominal Inequalities

4.1.1. 1. Set to Zero 2. Factor (solve for x intercepts) 3. Set intervals around Zeros 4. Chart test numbers on number line 5. Find intervals that match Inequalities 6. graph

### 4.2. Rational Inequalities

4.2.1. 1. Find Critical Numbers -Zeros -Undefined - can not divide by zero 2. Follow polynomial steps

## 5. 13.4

### 5.1. Equations in Quadratic Form

5.1.1. For Equations that Factor 1. Use u for b, u^2 for a - check squaring 2. Solve problem with substitution 3. Solve mini problems using what you substituted