pre calc gold sheet quiz

standard form for quadratics

ax²+bx+c c=y-int, vertex = (-b/2a, y)

Average ROC from x=a to x=b

Slope of secant line, old school slope → f(b)-f(a)/b-a

Intercept form for quadratics

y = a(x-p)(x-q) , p an q are zeros

vertext form for quadratics

y = a(x-h)²+k vertex = (H,k), AOS = X = h

concave up

“like a cup” ROC is increasing

Instantaneous rate of change at x=a

slope of tangent line, estimate by finding AROC of 2 pts near x=a

slope intercept form for linear functions

y=mx+b, m=slope, b=y-int

point slope form for linear functions

y-y1 = m (x-x1) m= slope, (x1, y1) = point

concave down

“Like a frown”, ROC is decreasing

standard form for linear functions

ax + by = c

fundamental theorem of algebra

a polynomial of degree n has a total of n zeros

quadratic formula

even function

f(x) = f(-x)

odd function

f(-x) = -f(x)

end behavior

horizontal asymptotes

Finding vertical asymptotes for a rational function

factor the denominator and find what makes it equal to zero

finding zeros of a rational function

factor the numerator and find out what makes only it =0

finding holes for rational functions

find what makes both numerator and denominator = 0

the binomial theorum

arithmetic sequences

geometric sequences

exponential functions

compound interest

compounded continuously

half - life problems

how to find an inverse f^-1

switch x and y, then solve for the new y

exponential relationship

inputs change additively, outputs change multiplicatively

logrithmic relationships

inputs change multiplicatively, outputs change logrithmically

semi log plots of exp, growth and exp. decay

linear w/ positive slope, and linear w/ negative slope

arc length formula

Building coterminal angles

All points on the unit circle

tan 0

csc 0

sec 0

cot 0

tan 0 represents

slope of terminal ray of angle 0

domain of y = tan 0

pythagorean identities

cos (U+-V)

sin (u+-v)

conversion equations w/ polar and rectangular coordinates

Polar Graphs (symmetry)

if equations has cos 0….

if equations has sin 0…

symmetric over polar axis

symmetric over y-axis

small circles

rose curves