CATA Unit 4 Concepts

how do you rewrite a function in vertex form?

find the vertex and you already have a

how do you find the vertex in standard form?

(-b/2a, f(-b/2a))

how do you find x-intercepts?

factor or do quadratic formula

what happens graphically as multiplicity increases?

it gets flatter towards the zero

what happens graphically when multiplicity is even?

bounces (but touches) x -axis

what happens graphically when multiplicity is odd?

crosses the x-axis

how do you know the degree of the polynomial?

largest exponent is the degree

how do you know the number of turning points?

one less than the degree / highest exponent

positive a odd exponenet end behavior

low left up on right

negative a odd exponent end behavior

up left low on right

positive a even degree end behavior

up left up right

negative a even degree

down left down right

how do you know multiplicity

power on top of factored form

vertex form

f(x) = a(x-h)² + k

standard form

f(x) = ax²+bx+c

how do you find the vertical asymptote?

its basically the domain, factor the denominator and solve

what if when you factor the function something is cancelled out?

that means there is a hole (removable discontinuity) in the graph and solved spot

horizontal asymptotes tell us about

the end behavior

what is the HA when

degree of num < degree of denominator

aka bottom heavy

y=0

what is the HA when

degree of num = degree of denominator

aka even

y = leading coefficient / leading coefficient

what is the HA when

degree of num > degree of denominator

aka top heavy

there is no HA

can there be a HA and a SA?

no

what does a slant asymptote tell us?

end behavior

(doesn’t influence area between two vertical asymptotes)

when do slant asymptotes exist?

only when the degree in the numerator is one more than the degree in the denominator

how do you find a slant asymptote?

divide the rational function but ignore remainder

how do you find x intercept in a rational function?

set numerator (top) equal to 0

how do you find y intercept in a rational function?

plug in x as 0

how do you find f(#) using synthetic division?

the remainder is the corresponding y/f(x)

complex zeros always

come in pairs, + and -

simplify

(x-a+bi)(x-a-bi)

(x-a)²-bi²