70606
Description
Quadratic Functions
- Quadratic formula
- Rootrs/Zeros
- Discriminant
- b^2-4ac
- Example if: if b^2-4ac=o we have no roots
- If b^2-4ac>o, we have two dinstinct roots
- if b^2<, we have two imaginary roots
- Example if: if b^2-4ac=o we have no roots
- b^2-4ac
- x=-b+-^.5 b^2-ac/2
- Rootrs/Zeros
- Standard form
- ax^2+bx+c=0
- To solve
- You can Factor it
- example
- x^2+-5x+4=0
- (x-4)(x-1)
- Example of finding the squares
- Example of finding the squares
- (x-4)(x-1)
- x^2+-5x+4=0
- example
- Or use
quadraic
formula
- You can Factor it
- To solve
- c value is the y-intercept
- Graphing
- changes in c
- if c>0, parabola moves up
- if c<0, the parabola moves down
- if c>0, parabola moves up
- changes in b
- b>0, vertex movs down and left
- b<0, vertex moves dow and right
- b>0, vertex movs down and left
- changes in c
- to get to vertex form you complet the square
- ax^2+bx+c=0
- Vertex form
- a(x-h)^2+k
- example
- a(3-1)+8
- if a is negitive, the parabla opens up
- if a is positive the graph opens down
- if a is negitive, the parabla opens up
- a(3-1)+8
- To slove
- Isolate 'x'
- Isolate 'x'
- H and K are = to vertex
- If a>0, vertex is minimum
- If a<, vertex is maximum
- If a>0, vertex is minimum
- changes in K
- if K>0, the parabola shifts up
- if k<0 the parabola shifts down
- if K>0, the parabola shifts up
- example
- changes in h
- if h>o, the parabola shifts right
- if h<o, the parabala shifts left
- if h>o, the parabola shifts right
- a(x-h)^2+k
- Factored form
- a(x-s)(x-t)
- example
- a(x-7)(x+7)
- a(x-7)(x+7)
- example
- To solve
- set each factor to = 0
- set each factor to = 0
- a(x-s)(x-t)
- Graphing
- Parabola
- Positive
- negitive
- Positive
- vertex
- x/y intercept
- x/y coordinats
- Translations
- horazontal
- vertical
- horazontal
- shift and step method
- Parabola
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