2.2
Quadratic
functions
• Quadratic equation:
y  Ax  Bx  C
2
• Use knowledge of quadratics to find maximum and
minimum values.
Quadratic functions can be used to
describe supply and demand curves,
profit, revenue, cost, and other
situations, quadratic functions can be
written in the form
f ( x)  ax  bx  c
2
Remember that the maximum or
minimum value of a quadratic function
occurs at the y of the vertex. x is where
the maximum or minimum occurs. The
vertex is the point   b
b 
, f ( )

2a 
 2a
Example
Let C(x) be the cost to produce x items
and R(x) be the revenue from x items.
(a) Graph both functions
(b) find the minimum break-even quantity,
(c) find the maximum revenue
(d) find the maximum profit.
R( x)  .5 x  8 x
C ( x)  1.5 x  15
2
Answers
B)3
C)$32
D)$6.13