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| Equation for parabola f(x)= 2(x-4)+8 |
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Definition
| F(x)= a(x-h) +k F(x)= 2(x-4)+8 (h=4, k=8 Vertex= (4,8) |
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| equation oof parabola f(x)= 3x^2 -8x +4 |
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Definition
f(x)=ax^2+bx+c vertex= x= -b/2a
y= F(-b/2a) 3x^2 -8x+4
-b=8 2a=2(3)=6 8/6=4/3 x=4/3 f(-b/2a)= f(4/3) 3(4/3)^2-8(4/3)+4= -4/3 y=-4/3 vertex= (4/3,-4/3) |
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| opens up or down ----leading coeffient |
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| non ngitive or raction integers |
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| largest exponent ex. Ax^3+ Bx^7+Cx^4 degree =Bx^7 = 7 |
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| leading coeffient test to determine end behavior |
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Definition
| ax^even = rise rise -ax^even = fall, fall (f(x)=x^2or parabala) ax^odd = fall rise -ax^odd = fall rise (f(x)= x^3 or cubic) |
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Definition
f(x) = 0 (x-int)
ex. f(x)=3(x+5)(x+2)^2 zero's= -5 with multplicity of 1 which is odd so it crosses at -5 and zeros at -2 with multiplicty of 2 which is even so it crosses at -2 |
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| Rational equations f(x) = p(x)/q(x) |
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Definition
Den ≠ 0
Veritcal Asymptote |
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Definition
veritcle Symptote = -5
b/c x+5=0 x=-5 and the den cannot equal o so this is where the VA is. |
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Definition
n< m ------y=0
n=m ------ leading coeff/leading coeff
n>m no HA |
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| determine symetry for f(x)= p(x)/q(x) |
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Definition
f(x)=f(-x) y axis symetry
f(x)= -f(x) origin symetry
if some change but not all then not symetirc to y or origin |
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p(x)=o = X int [top = 0]
q(x)=0 = V/A. [bottom =0] |
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Definition
1) set = to 0 on right
2) factor
3) get crit #
4) build sign chart with crit# as boundry pts
5) fill in test #s
6 determine correct interval (>0 means pos and <0 means neg)
7) write answer in interval notion (-∞,# )] U [(#,∞)] |
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