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Quadratic Functions by Mind Map: Quadratic Functions
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Quadratic Functions

Standard Form y=a(x-h)²+k

Graphing

domain and range

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

function, Vertical line test

(h,k) = vertex

if a>0, vertex is the minimum

if a<0, vertex is the maximum

x=h is the axis of symmetry

General Form y=ax²+ bx + c

Graphing

domain and range

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

function, vertical line test

Completing the square

Univariate polynomial equation with degree 2

c is the y-intercept

Quadratic formula

roots/zeros

discriminant

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

Quadratic Equation

set function equal to 0