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