Section+2.1

2.1

**Linear & Quadratic Functions**
Polynomial Function: f(x) = anxn + an-1xn-1 +. . . + a1x + a0 where an is called the leading coefficient and has a degree of 'n'. ex. Polynomial or not? f(x) = 4x^3 - 5x +1/2 YES g(x) = 6x^-4 - 7 NO h(x) = √(9x^4 + 16x^2) NO NAMES: (take the highest exponent) f(x) = 0 degree: undefined zero function f(x) = a (a≠0) degree: zero constant function f(x) = ax+b (a≠0) degree: one linear function f(x) = ax2 + bx + c (a≠0) degree: two quadratic function

Linear Function: y=mx+b m=slope b=y-intercept slope = rate of change (y2-y1) / (x2-x1) Lines have a constant rate of change m=0 horizontal m=undefined vertical positive slope uphill negative slope downhill

Example: Write an equation for the linear function f suich that f(-1)=2 and f(3)=-2 The points are (-1,2) and (3,-2) Solution: m= (2 - -2) / (-1 - 3) y=mx+b 2=-1(-1)+b 2=1+b b=1 Answer: y= -1x+1

Quadratic Functions: y=ax2 + bx + c (Standard Form) if a>0 it opens upward if a<0 it opens downward

Finding the vertex: 1. y=ax2 + bx + c -(b/2a), f(-(b/2a)) 2. vertex form: a(x-h)^2+k (h,k)

Example. Find the vertex, axis of symmetry, then rewrite in vertex form. f(x) = 6x-3x^2-5 Solution: = -3x^2+6x-5 = -6/2(-3) vertex: (1,-2) USE METHOD 1. FROM ABOVE axis of symmetry: x=1 vertex form: y=a(x-h)^2+k y= -3(x-1)^2-2

Terms: Axis of Symmetry: a vertical line through the vertex in which the graph is symmetric.

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