Pre-Cal Chapter 2 Polynomial, Power, and Rational Functions Section 2.1

Definitions Cont. Linear Correlation: when the points of a scatter plot are grouped together such that they look to be in a line. Linear Correlation: when the points of a scatter plot are grouped together such that they look to be in a line. Positive Linear Correlation: when the line of correlation is increasing. Positive Linear Correlation: when the line of correlation is increasing. Negative Linear Correlation: when the line of the correlation is decreasing. Negative Linear Correlation: when the line of the correlation is decreasing.

Definitions Polynomial Function: Must have a leading coefficient that is > 0 and have an exponent that is not a fraction. Polynomial Function: Must have a leading coefficient that is > 0 and have an exponent that is not a fraction. Degree of a Polynomial Function: the highest exponent on your variable. If there is no variable and the number of the function is ≠0 the degree is zero. If it is = 0 then it is undefined. Degree of a Polynomial Function: the highest exponent on your variable. If there is no variable and the number of the function is ≠0 the degree is zero. If it is = 0 then it is undefined. Linear Function: a polynomial function with degree of 1 Linear Function: a polynomial function with degree of 1 Constant Term: the term in the function that does not have a variable attached to it. Constant Term: the term in the function that does not have a variable attached to it.

Formulas Linear Function: f(x) = mx + b Linear Function: f(x) = mx + b m = to find b:

Quadratic Function: a polynomial function of degree 2. Quadratic Function: a polynomial function of degree 2. Standard Quadratic Function: Standard Quadratic Function: f(x) = ax 2 + bx + c Quadratic Vertex Form: f(x) = a(x - h) 2 + k; where (h, k) is your vertex of the quadratic. Quadratic Vertex Form: f(x) = a(x - h) 2 + k; where (h, k) is your vertex of the quadratic. Axis of Symmetry (Axis): the line of symmetry for a parabola. The x from your vertex Axis of Symmetry (Axis): the line of symmetry for a parabola. The x from your vertex Vertex: (h, k) Vertex: (h, k) graphically: the absolute maximum or minimum of your parabola. Algebraically: (-b/2a, f(h))

Putting a Quadratic in Vertex Form: Uses a form of Completing the Square OR Uses a form of Completing the Square OR Take out Leading Coefficient and plug in Take out Leading Coefficient and plug in vertex (-b/2a, f(h)) for y = a (x – h) 2 + h EX) y = x 2 + 4x – 7 EX) y = 2x 2 + 7x + 5