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## 1. General Form y=ax²+ bx + c

### 1.1. Graphing

1.1.1. domain and range

1.1.2. transformations

1.1.2.1. changes in a (vertical stretch)

1.1.2.1.1. if a>0, the parabola opens up

1.1.2.1.2. if a<0, the parabola opens down

1.1.2.1.3. if -1<a<1 and a≠0, the parabola widens

1.1.2.1.4. if a>1 or a<-1, the parabola narrows

1.1.2.2. changes in b

1.1.2.2.1. b<0, vertex moves down and right

1.1.2.2.2. b>0, vertex moves down and left

1.1.2.3. changes in c

1.1.2.3.1. c>0, parabola moves up

1.1.2.3.2. c<0, parabola moves down

1.1.3. function

1.1.3.1. vertical line test

### 2.2. discriminant

2.2.1. b²-4ac

2.2.1.1. if b²-4ac=0, we have one distinct root

2.2.1.2. if b²-4ac>0, we have two dinstinct roots

2.2.1.3. if b²-4ac<0, we have two imaginary roots

## 3. Standard Form y=a(x-h)²+k

### 3.1. Graphing

3.1.1. domain and range

3.1.2. transformations

3.1.2.1. changes in a

3.1.2.2. changes in h

3.1.2.2.1. h>0, parabola shifts right

3.1.2.2.2. h<0, parabola shifts left

3.1.2.3. changes in k

3.1.2.3.1. k>0, parabola shifts up

3.1.2.3.2. k<0, parabola shifts down

3.1.3. function

3.1.3.1. Vertical line test

### 3.2. (h,k) = vertex

3.2.1. if a>0, vertex is the minimum

3.2.2. if a<0, vertex is the maximum

3.2.3. x=h is the axis of symmetry