Asymptotes
- the graphs of rational equations in the form y = \(\frac{a}{x-k}\ +h\), where a, k, and, h are constants and k doesn't equal x, have the line x = k as a vertical asymptote and the line y = h as a horizontal asymptote
- \(y=a\cdot b^x\), a= inital value so teh graph crosses the y axis at 0,a; and if a> 0 and b > 1 the graph much be increasing.
- f(x)=a^x+v; v= shift of graph left/right
parabola
- y=a(x−h)2+k with the vertex of (h,k); and an axis of symetry of x=h; if a > 0 the parabola opens up and has a min value, if a < 0 the parabola oopens down and has a max value
- Vertex From: a(x-h)2 +k , where h,k is the vertex, x=h is the axis of symetry, h represents a horizontal shift, and k represents a vertical shift
- in vertex form h=-b/2a and k = f(h)
Graphed Quadratics
- \(y=a\left(x-r_1\right)\left(x-r_2\right)\); x intercept at r1,0 and r2,0
Extra
reflect by -x or -y to flip axis
Algebraic Transformations
- x2 + x represents a vertical shift in that direction
- (x+2)2 represents a horizontal shift of - 2
- 2x2 is a vertical stretch
- (2x)2 is a horizontal stretch