If n is greater than m
There is no horizontal asymptote
Axis of Symmetry (Vertex form)
x=h
Vertex (Vertex form)
(h,k)
Vertex form equation
A(x-h)^2 + k
Which one is n and which one in m
N is the top variable
m is the bottom variable
Axis of Symmetry (standard form)
x = (-b/2a)
Domain of a polynomial function
Set the denominator equal to zero and solve
Standard form equation
Ax2+bx+c
Vertical asymptote
- the domain unless it is a hole
- if the domain is all real numbers or all real numbers except for zero then there is no vertical asymptote
If n equals m then
Y = a / b
If n is less than m
Then horizontal asymptote is zero
X-Intercept (Vertex Form)
f(x) = 0, solve 0+a(x-h)^2 +k
How to check for a hole
Factor.
If they are both on top and bottom and cancel out, then it is a hole
X intercept of a polynomial function
Set numerator equal to zero and solve
Find max and min
2nd trace, calc max or min
X- Intercept (standard form)
f(x) = 0 solve ax^2+bx+c = 0
Y intercept of polynomial function
F (0)
Y-Intercept (Vertex form)
x=0 ; f(0) a(0-h)^2+k
Y- Intercept (standard form)
(0,c)
Horizontal asymptote
Follow rules regarding n to m
Vertex (standard form)
(-b/2a , f(-b/2a) )
Domain:
Set numerator equal to zero.
Use quadratic formula to solve
If it’s only x^2 the domain is zero.
Which one is n and which one in m
N is the top variable
m is the bottom variable
Domain:
Set numerator equal to zero.
Use quadratic formula to solve
If it’s only x^2 the domain is zero.
Horizontal asymptote
Follow rules regarding n to m
If n equals m then
Y = a / b
If n is less than m
Then horizontal asymptote is zero
Vertical asymptote
- the domain unless it is a hole
- if the domain is all real numbers or all real numbers except for zero then there is no vertical asymptote
If n is greater than m
There is no horizontal asymptote
How to check for a hole
Factor.
If they are both on top and bottom and cancel out, then it is a hole