2.10
2
Graph y = ax + c
2.10-2.11 Quiz: Friday
Midterm: March 11
Vocabulary
• A quadratic function is a nonlinear (not a
line) function that can be written in the
standard form y = ax2+ bx + c where a ≠ 0
• Every quadratic function has a U-shaped
graph called a parabola.
Vocabulary
• The most basic quadratic function in the
family of quadratic functions, called the
parent quadratic function, is y = x2
X
-2
Y= 4
-1
0
1
2
1
0
1
4
Parts of a Parabola
• The lowest or highest point on a parabola
is the vertex.
• The line that passes through the vertex
and divides the parabola into two
symmetric parts is called the axis of
symmetry.
Graph y = ax2
• The coefficient “a” can stretch or shrink the
graph.
• If “a” is negative then the graph flips
upside down.
(Or as I like to call it…makes a SAD face)
Example 1:
• Graph y = 2x2. Compare the graph with
the parent function, y = x2.
– You need to make a table of values.
X
Y=
-2
-1
0
1
2
You Try:
• Graph y = 1/2x2. Compare the graph with the
parent function, y = x2.
X -2 -1 0
1
Y=
2
Example 2:
• Graph y = -3x2. Compare the graph with
the parent function, y = x2.
– You need to make a table of values.
X
Y=
-2
-1
0
1
2
Graph y = ax2 + c
• The constant “c” moves the graph up or
down.
– If “c” is positive it moves the graph up
– if “c” is negative it moves the graph down.
Example 4:
• Graph y = x2 + 2. Compare the graph with the
parent function, y = x2.
– You need to make a table of values.
X
Y=
-2
-1
0
1
2
You Try:
• Graph y = x2 – 4. Compare the graph with
the parent function, y = x2.
Homework:
• P. 100 # 1-9all, 16, 17, 20, 21