Quadratic Functions

owensharks
Mind Map by , created over 6 years ago

Quadratic functions Mind Map on Quadratic Functions, created by owensharks on 05/04/2013.

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owensharks
Created by owensharks over 6 years ago
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Quadratic Functions
1 Quadratic formula
1.1 Rootrs/Zeros
1.2 Discriminant
1.2.1 b^2-4ac
1.2.1.1 Example if: if b^2-4ac=o we have no roots
1.2.1.2 If b^2-4ac>o, we have two dinstinct roots
1.2.1.3 if b^2<, we have two imaginary roots
1.3 x=-b+-^.5 b^2-ac/2
2 Standard form
2.1 ax^2+bx+c=0
2.1.1 To solve
2.1.1.1 You can Factor it
2.1.1.1.1 example
2.1.1.1.1.1 x^2+-5x+4=0
2.1.1.1.1.1.1 (x-4)(x-1)
2.1.1.1.1.1.1.1 Example of finding the squares
2.1.1.2 Or use quadraic formula
2.2 c value is the y-intercept
2.3 Graphing
2.3.1 changes in c
2.3.1.1 if c>0, parabola moves up
2.3.1.2 if c<0, the parabola moves down
2.3.2 changes in b
2.3.2.1 b>0, vertex movs down and left
2.3.2.2 b<0, vertex moves dow and right
2.4 to get to vertex form you complet the square
3 Vertex form
3.1 a(x-h)^2+k
3.1.1 example
3.1.1.1 a(3-1)+8
3.1.1.1.1 if a is negitive, the parabla opens up
3.1.1.1.2 if a is positive the graph opens down
3.1.2 To slove
3.1.2.1 Isolate 'x'
3.1.3 H and K are = to vertex
3.1.3.1 If a>0, vertex is minimum
3.1.3.2 If a<, vertex is maximum
3.1.4 changes in K
3.1.4.1 if K>0, the parabola shifts up
3.1.4.2 if k<0 the parabola shifts down
3.2 changes in h
3.2.1 if h>o, the parabola shifts right
3.2.2 if h<o, the parabala shifts left
4 Factored form
4.1 a(x-s)(x-t)
4.1.1 example
4.1.1.1 a(x-7)(x+7)
4.2 To solve
4.2.1 set each factor to = 0
5 Graphing
5.1 Parabola
5.1.1 Positive
5.1.2 negitive
5.2 vertex
5.3 x/y intercept
5.4 x/y coordinats
5.5 Translations
5.5.1 horazontal
5.5.2 vertical
5.6 shift and step method

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