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Precalculus: Section 3.1-3.2
Precalculus: Section 3.1-3.2
39
Mathematics
Undergraduate 1
10/12/2015

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Term
Quadratic Function
Definition
f(x)=ax^2+bx+c
Term
Quadratic Function (Standard Form)
Definition
f(x)=a(x-h)^2+k
Term
Power Function
Definition
f(x)=ax^n
Term
What Are The Steps To Graphing A Standard Form Quadratic Function?
Definition
1.) Know That It is A Parabola
2.) Determine How The Parabola Opens
3.) Find The Vertex (h,k)
4.) Find the X-Intercepts If Any
Term
How Do You Determine How A Parabola Opens For a Quadratic Function?
Definition
a>0 It Opens Up
a<0 It Opens Down
Term
Quadratic Functions Have A Minimum Or Maximum Value k at ____
Definition
x=h
Term
How Do You Find X-Intercepts In a Quadratic Function In Standard Form?
Definition
1.) Solve For a(x-h)^2+k=0
2.) If They Are Real Numbers They Are X-Intercepts
3.) If Not and a>0, Then The Parabola Lies Above The X-axis
4.) If Not and a<0, Then The Parabola Lies Below The X-axis
Term
How Do You Find The Y-Intercept In A Quadratic Function In Standard Form?
Definition
Solve For f(0)=ah^2+k
Term
How To Convert A Quadratic Function Into Standard Form?
Definition
x^2+(b/a)x+(b^2/4a^2)
Term
How to Find The Vertex of A Quadratic Function?
Definition
1.) h=-b/2a
2.) k=c-(b^2/4a)
Term
What Are The Steps To Graphing A Quadratic Function?
Definition
1.) Identify a,b,c
2.) Determine How The Parabola Opens
3.) Find The Vertex
4.) Find The X-Intercepts If Any
5.) Find The Y-Intercept
6.) Find The Axis Symmetry
Term
How to Find The X-Intercept of a Quadratic Function?
Definition
1.) Solve For ax^2+bx+c=0
2.) If They Are Real Numbers They Are X-Intercepts
3.) If Not and a>0, Then The Parabola Lies Above The X-axis
4.) If Not and a<0, Then The Parabola Lies Below The X-axis
Term
How To Find The Y-Intercept of A Quadratic Function?
Definition
It's C
Term
How To Find Axis Symmetry For A Quadratic Function?
Definition
Solve for x=-b/2a
Term
What is the range of a quadratic function?
Definition
If a>0, [k,infinity)
If a<0, (-infinity,k]
Term
What Shape Does f(x)=x^2 Make?
Definition
A Parabola
Term
What Shape Does -|a|x^2 Make?
Definition
A Parabola Flipped Over the X-Axis Pointing Downward
Term
f(x)=a(x-h)^2+k
Definition
K= Vertical Movement
H= Horizontal Movement
A= Reflection (Slope)
Term
Let L be a horizontal line and (a,b) a point then a parabola is...
Definition
the set of points equal distance from L and (a,b)
Term
Examples of Polynomials
Definition
Linear Functions
Quadratic Functions
Constant Functions
Power Functions
Term
Linear Function
Definition
f(x)=ax+b
Term
f(x)=a
Definition
Constant Function
Term
f(x)=ax^n
Definition
Power Function
Term
What is the degree of f(x)=2x
Definition
0
Term
What is the Degree of f(x)=0
Definition
-1 or no degree
Term
n
Definition
degree
Term
Leading Term
Definition
a(sub"n")X^n [If factored into parts multiply the leading term of each part together to form the overall leading term]
Term
Leading Coefficient
Definition
a(sub"n")
Term
Polynomials are ____ and _____
Definition
Smooth
Continuous
Term
"Smooth" In Reference to Polynomials...
Definition
Means No Corners
And No Cusps (Curved Corner)
Term
In the power function where the degree is positive....
Definition
It Behaves like x^2: Parabola
Term
In the power function where the degree is negative....
Definition
It Behaves Like x^3: Dancing Arms
Left Down, Right Up
Term
End Behavior
Definition
What happens to f(x) when
x goes to infinity
or
x goes to negative infinity
Term
How Do You Find End Behavior?
Definition
1.) Figure out what the graph for the leading term looks like to determine what happens to f(x) when x goes to infinity or negative infinity
Term
What Does 1/x^2 appear as on a graph?
Definition
A Positive Ghost
Term
What Does 1/x appear as on a graph?
Definition
A Diagonal Omnitrix Symbol
Term
What is your constant term?
Definition
It is a normal number at the end of a polynomial or just a zero (If It is In Factored Form You Multiply the normal numbers of each part to form it)
Term
When you multiply exponents they..
Definition
Add Together
Term
If you don't know what the graph looks like and you are finding the end behavior..
Definition
You use common sense and replace the leading term with infinity, duh
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