Standard Form
Quadratic Function
 Highest degree is 2.
 Its graph is called a parabola.
f ( x)  ax  bx  c
2
quadratic term
linear term
constant term
Example 1:
a. Consider the quadratic function f(x) = 2 – 4x + x2. Find the y-intercept,
the equation of the axis of symmetry, and the x-coordinate of the vertex.
b. Make a table of values that includes the vertex.
c. Use the information from parts A and B to graph the function. What are
the domain and range of the function?
Domain & Range
Example 2:
Consider the function f(x) = –x2 + 2x + 3. State the
maximum or minimum value of the function.
Example 3:
Consider the function f(x) = x2 + 4x – 1. Determine
whether the function has a maximum or a minimum
value.
A. maximum
B. minimum
C. both
D. none
Example 4:
Which is the graph of f(x) = 2x2 + 3x + 2?
A.
B.
C.
D.
Example 5:
Consider the quadratic function f(x) = 3 – 6x + x2. Find the
y-intercept, the equation of the axis of symmetry, and
the x-coordinate of the vertex. Then graph the function.
Example 6:
Consider the function f(x) = x2 + 4x – 1. What are the
domain and range of the function?
Example 7:
The path of a diver is approximated by feet in the figure
shown and the equation given. What is the maximum
height of the diver? Approximately how long did it take
the diver to reach his maximum height?
4 2 24
h(t )   t  t  12
9
9
Example 8:
a. ECONOMICS A souvenir shop sells about
200 coffee mugs each month for $6 each. The shop
owner estimates that for each $0.50 increase in the
price, he will sell about 10 fewer coffee mugs per month.
How much should the owner charge for each mug in
order to maximize the monthly income from their
sales?
Example 8:
b. What is the maximum monthly income the owner can
expect to make from these items?
Calculator Steps
Finding the Vertex
- Input equation into y=
- 2nd >> trace >> minimum or maximum
- Min or Max will depend on the direction of the parabola
- Move the flashing cursor to the left of the vertex and
press enter
- Repeat for the right side of the vertex
- Press enter for a 3rd time to have calculator “Guess?”
the vertex point.
Calculator Steps
Finding the X-intercept
- Input equation into y=
- 2nd >> trace >> zero
- Move the flashing cursor to the left of the x-intercept
and press enter
- Repeat for the right side of the x-intercept
- Press enter for a 3rd time to have calculator “Guess?”
the vertex point.