2­2 Notes
­
Quadratic functions
Standard form: a>0 opens U p To find x­ints
g(x) = a(x − h)2 + k a <0 opens dow ⋂ y=0, solve for x
Vertex (min or max) =
(h,k)
y = x2
Horizontal shift = h !!
Vertical shift = k
What is the
equation for the
parabola to the
left?
a < 1 stretch
a > 1 shrink
To find y­int
x=0, solve for y
The vertex
of a parabola
is either a
max or a min!
Find the shifts, vertex, x­ints, y­int, and graph each of the following:
f (x) = (x + 3)2 − 1
g(x) = − 2(x − 3)2 + 8
h(x) = (x − 2)2 + 1
j (x) = x2 + 3 horiz:_________
vert:__________
vertex:________
y­int:_________
horiz:_________
vert:__________
vertex:________
y­int:_________
horiz:_________
vert:__________
vertex:________
y­int:_________
horiz:_________
vert:__________
vertex:________
y­int:_________
x­ints _________
x­ints _________
x­ints _________
x­ints _________
Quadratic formula → for the form: ax2 + bx + c = 0
Example 1: f (x) = − x2 − 2x + 1
Example 2: g (x) = 3 + 6x + x2
Vertex
b
b
x =− 2a
, y = f (− 2a
)
Won’t be provided on a quiz but
very useful for decimals!!
ex1
Ex 1
Ex 2
ex2
for x­intercepts & factors
−b ± √b2 −4ac
x=
2a
Maximize/Minimize
Steps:
1. Write an equation for the
max/min, and any other
equation given.
2. Solve for one variable in
an equation
3. Substitute for that
variable
4. Write the equation for
the quadratic formula
5. Calculate the vertex (will
be the max or min
Ex 1 In a pair of numbers
whose difference is 10, find
the pair of numbers whose
product is as small as
possible.
Ex 2 You have 100 yards
of fencing to enclose a
rectangular region. Find
the dimensions of the
rectangle that maximize
the enclosed area. What is
the area?