Chapter 2 Section 1 - Quadratic Functions

• A polynomial function is of the form:
• f(x)=AnX^n+An-1X^n-1+An-2X^n-2+...+A2X^2+A1X+A0
• Quadratic Formula
• http://www.youtube.com/watch?v=H_7lNT9oDzI
• The value of n must be a nonnegative integer (i.e., it must be a whole number; it is equal to zero or a positive integer)
• The coefficients are An, An-1, ... A1, A0. <-- These are real numbers
• The degree of the polynomial function is the highest value of n
• f(x)=X^2+5X-7 (second degree)
• g(x)=2X^3-8+/X[square root of X]-1 (not a polynomial)
• h(x)=X^1/2+X-6 (not a polynomial)
• i(x)=4 (zero degree)
• k(x)=2^x (exponential function)
• Degree               |Name               |Example          

                     0             Constant            f(x)=4
                     1             Linear                g(x)=5x-3
                     2             Quadratic          h(x)=3x^2-9x+8
                     3             Cubic                i(x)=x^3
                     4             Quartic              j(x)=x^4
                     5             Quintic              k(x)=x^5

• Zeros, X-intercepts, f(x)=0, roots <-- All mean the same thing
• Standard form: f(x)=ax^2+bx+c
• Vertex form: f(x)=a(x-h)^2+k
• a: stands for the shrinking or stretching of the parabola
• h: determines whether it moves left or right
• k: symbolizes if it goes up or down
• Completing the square
• f(x)=x^2-6x+5
• f(x)=(x^2-6x+__)                                            +5
• take the +5 and put it far away from the equation, it'll be used later
• to find the square use the equation ((b/2)^2)
• f(x)=(x-3)^2 --> f(x)=(x^2-6x+9)+5
• seeing as f(x) isn't a number, because you add 9 to one side, you still have to subtract it
• that's were the last digit comes in
• f(x)=(x^2-6x+9)+(-9+5)
• f(x)=(x-3)^2-4
• vertex: (3,-4)

Homework: 2.1-#1-8, 12, 17, 20, 29, 31, 35, 37, 41, 54, 61, 65, 67, 69