ch 3 - 4 study guide Essay

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3.1
Find slope: y2-y1/x2-x1
Find slope of the line joining the points (2,5) and (-1,3)
5-3
2-(-1) = 2/3 Slope =2/3

Quadratic:
Vertex formula: (-b/2a)
Completing the square to find vertex:
F(x)=2x^2 +12x-3 2
(f(x)=x^2 +6x-1.5) 2 2 f(x)=2(X+3)^2 – 21
Vertex = (-3,-21)
To find x – intercepts use quadratic formula

Area of a field:
400 yrds of fencing – rectangular fence p=2l+2w a=lw
2l+2w=400 a=(200-w)w l+w=200 a=-w^2 +200w l=200-w Polynomial:
Degree:
Highest when not factored
Add together when factored
N-1 gives the max turning points
Multiplicity is what happens at the x-intercepts

Long Division: X^2 +x-4 r5
X+1| x^3 +2x^2 -3x+1 -x^3 –x^2 x^2-3x -x^2 –x -4x+1 +4x+4 5

Asymptotes:

Finding the Domain/vertical asymptote:
F(x)=x+2 {x|x≠3} x-3 Domain is where the bottom = zero x=3 is the vertical asymptote

Finding the Horizontal asymptote:
If the degree of the top and bottom are equal, the ratio of the leading coefficients is the horizontal asymptote.
If the degree of the bottom is greater than the degree of the top, then y=0 is the horizontal asymptote.
Finding the oblique asymptote:
If the degree of the top is one degree greater then the degree of the bottom.
Finding the holes in the graph:
When a factored equation can cancel out.
F(x)=2x^2 -5x-12 = (2x+3)(x-4) = 2x+3 3x^2 -11x-4 = (3x+1)(x-4) = 3x+1
Domain:

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