Chapter Sections 3.1 & 3.2 Flashcards
What is the vertex form equation?
F(x)=a(x-h)^2+k
What is the standard form equation?
F(x)=ax^2+bx+c
What are other words for zeros
X int, root, solutions
What is the quadratic formula
-b+/- square root of (b^2-4ac) all over 2a
What is the discriminant
B^2-4ac
What does it mean if the discriminant is greater than zero
2 x intercepts
What does it mean if the discriminant is equal to zero
1 x intercept
Perfect square trinomials hit x axis how many times
Once
What does it mean if the discriminant is less than zero
No x intercept
How do you complete the square? Ex) f(x)=x^2-6x-1
Make it look like this: f(x)=(x^2-6x ___) -1
Divide the -6 by 2 which would give you -3
Then square the - 3 to get 9
Add 9 after -6x and subtract from end too
Then simplify everything
In a polynomial n is a ______ integer
A nonnegative integer
What would make you see that it a function can’t be a polynomial
1/x or
square root of x
or y= |x|
What is continuous polynomial versus discontinuous polynomial
Continuous has no gaps or holes. If does not meet these standards then it is discontinuous
If n is even what are some characteristics of the graph (only for parent functions!!!)
- symmetric about y axis so EVEN
- domain: (-infinity, infinity)
- range: [0,infinity)
- contains the points (0,0) (1,1) (-1,1)
If n is odd then what are some characteristics of the graph (only for parent functions!!!!)
- symmetric about the origin so ODD
- domain AND range = (-infinity,infinity)
- contains the points (0,0) (1,1) (-1,-1)
What is the multiplicity?
The number of times a zero occurs
What is the multiplicity of these examples
- (x-1)
- (x-1)^2
- (x-1)^3
1, 2, and 3
Odd multiplicity does what
Even multiplicity does what
Odd = crosses x axis Even= touches x axis
Turning points are also known as…
Local min and local max
What is the notation for end behavior…
As x -> ____ , f(x) -> _____
For end behavior
If degree is even and a>0 then
As x -> negative infinity, f(x) -> positive infinity
As x -> positive infinity, f(x) -> positive infinity
For end behavior
If degree is even and a<0 then…
As x -> negative infinity, f(x) -> negative infinity
As x -> positive infinity, f(x) -> negative infinity
For end behavior
If degree is odd and a> 0 then…
As x -> negative infinity, f(x) -> negative infinity
As x -> positive infinity, f(x) -> positive infinity
For end behavior
If degree is odd and a<0 then…
As x -> negative infinity, f(x) -> positive infinity
As x -> positive infinity, f(x) -> negative infinity
