Suppose you need to find a quadratic function that has x-intercepts at
x = 0
and
x = 2
and a maximum value of 3.
(a)
A function in standard form that has parameters
a =
and
k =

has a maximum value of 3.
(b)
To obtain intercepts that are separated by 2 units, change the value of a from part (a) to
a =

(c)
To shift the x-intercepts to
x = 0
and
x = 2,
set
h
to
h =

(d)
Then, in the standard form equation of the quadratic function, the values of the parameters that meet the given criteria are
a
=
h
=
k
=
(e)
In the expanded form equation of the quadratic function, the values of the parameters that meet the given criteria are
a
=
b
=
c
=