Quadratic Functions
Completing the Square
Turn standard to vertex form
Steps:
Vertex Form
Graphing Easy!
vertex= (h,k)
+/- tells opening up or down
"a" is stretch factor
go up/down a, 4a, 9a...
x-intercenpt
y=0
Solve
one x term= isolating
everything in reverse
reverse operations
reverse order: SAMDEB
opposite of squaring is +/- square root
y-intercenpt
x=0
evaluate
Standard Form (General Form)
to graph, complete the square
factor out "a" from first two terms
add and - "special numbers"
(b/2)^2
bring - special number out of bracket
multiply by "a"
factor and simplify
analogy "gate keeper" on brackets
simplifying square roots
look for perfect square factors
ex: 20=5 x 4
perfect squares
Max/Min
find peak/valley
vertex
Have Equation
get vertex form
completing the square
To Get Equation
interpret the vertex
Define variables
sketching situation
What do you want to maximize/minimize?
create basic equation from this
extra info to sub in and get 1 variable
axis of symmetry
x=h
congruent equation
y=ax^2
get equation from graph
vertex in
find "a"
(h,k)
replace (x,y)
any other point on graph
solve for a
rewrite equation with a, h, k filled in