Quadratic Functions

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Quadratic Functions by Mind Map: Quadratic Functions

1. General Form y=ax²+ bx + c

1.1. Graphing

1.1.1. domain and range

1.1.2. transformations changes in a (vertical stretch) if a>0, the parabola opens up if a<0, the parabola opens down if -1<a<1 and a≠0, the parabola widens if a>1 or a<-1, the parabola narrows changes in b b<0, vertex moves down and right b>0, vertex moves down and left changes in c c>0, parabola moves up c<0, parabola moves down

1.1.3. function vertical line test

1.2. Completing the square

1.3. Univariate polynomial equation with degree 2

1.4. c is the y-intercept

2. Quadratic formula

2.1. roots/zeros

2.2. discriminant

2.2.1. b²-4ac if b²-4ac=0, we have one distinct root if b²-4ac>0, we have two dinstinct roots 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 changes in a changes in h h>0, parabola shifts right h<0, parabola shifts left changes in k k>0, parabola shifts up k<0, parabola shifts down

3.1.3. function 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

4. Quadratic Equation

4.1. set function equal to 0