math with ms k. quadratics in vertex form

what is the vertex form?

y = a(x - h)² + k

what does a control?

the vertical stretch

what does h control

the horizontal shift

what does k control

the vertical shift

if a > 0 the graph opens..

up

if a < 0 the graph opens..

down

a > 1 or a < -1 also means

when the absolute value of a is bigger than one

a > 1 or a < -1 does what to the graph

vertical stretch by a factor of a, making it skinnier

-1 < a < 1 does what to the graph?

vertically compresses the graph by a factor of a

if h > 0

shifts the graph h many units right

if h < 0

shifts the graph h many units left

if k > 0

shifts up by k units

if k < 0

shifts down by k units

the vertex is at?

(h, k)

the axis of symmetry is at?

x = h

always give your answer for the axis of symmetry as..?

an equation!!! (x = 2)

the domain of all quadratic functions is?

x is any element of the real (just do the fancy R)

the range depends on..?

location of the vertex

what two points do you need to find the vertex form equation of a parabola?

the vertex to act as h and k, and any other random point to act as x and y

steps to find vertex form equation when given points

1) input vertex form with the known points and variables
2) solve with algebra bedmas
3) write full concluding sentence

steps to find graph when given vertex form equation

1) table of values with vertex in the middle
2) input and do math
3) boom!

if the discriminative is positive?

2 real roots

if disc is zero?

one real root

if disc is negative?

no real roots

what is the discriminate of the quad formula

the part under the radical (b²-4ac)