Math Test #1

point-slope form

f(x)=y₀+m(x-x₀)

slope-intercept form

y=mx+b

quadratic discriminant rule

if d>0, 2 x-intercepts; if d=0, 1 x-intercept; if d<0, 0 x-intercepts

a in a quadratic

determines whether a parabola opens up or down + the steepness of the parabola

b in a quadratic

determines the location of the vertex

c in a quadratic

determines the y-intercept of a quadratic

quadratic vertex form

q(x)=a(x-h)²+k

leading term and coefficient

term with the highest n-value; the coefficient of that term

number of possible bends in a polynomial

n-1, though there could be fewer with multiplicity

polynomial end behavior

if degree is even, end behaviors are on the same side of the x-axis; if L.C. is positive, the behavior on the right side is increasing

rational functions

the quotient of two polynomials

domain of a rational function

all real numbers except when q(x)=0

zeros/roots/intercepts in a rational function

exist if r(x)=0, p(x)=0, and q(x)=/0

holes in a rational function

exist if p(x)=0, q(x)=0, and multiplicity in the numerator is greater than in the denominator

vertical asymptote

a vertical line that a function's graph gets closer and closer to, but never touches or crosses

vertical asymptotes in rational functions

exist if q(x) has a root with larger multiplicity than p(x)