April 01, 2014
Identifying Quadratic
Functions
Ch. 9-1
April 01, 2014
Warm-up
Find the values for y when,
x
y
-2
-1
0
1
2
Warm-up:
. Graph.
April 01, 2014
Identifying Quadratic Functions:
A quadratic function is any function that can be
written in the standard form y =ax2 + bx + c, where a,
b, and c are real numbers and a≠ 0.
**NOTE: Only a≠ 0; however, b and c may equal 0
Determine whether each function is quadratic:
1.
→ _____________________
YES or NO
April 01, 2014
Determine whether each function is quadratic:
2.
→ _____________________
YES or NO
3.
→ _____________________
YES or NO
April 01, 2014
Determine whether each function is quadratic:
4.
5.
6.
→ _____________________
YES or NO
→ _____________________
YES or NO
→ _____________________YES
or NO
April 01, 2014
Parabola:
The graph of a quadratic function is a curve called
a parabola. To graph a quadratic function,
generate enough ordered pairs to see the shape of
the parabola. Then connect the points with a
smooth curve.
Use a T- table to graph each quadratic function.
x
7.
-2
-1
0
1
2
y
April 01, 2014
Use a T- table to graph each quadratic function.
8.
x
-2
-1
0
1
2
y
April 01, 2014
Direction of a Parabola:
Some parabolas open upward and some open downward.
Look at #7 & #8.
What is the difference between the two quadratic functions?
__________________________
Make a prediction:
o A parabola opens upward when __________________________
o
A parabola opens downward when ________________________
April 01, 2014
Tell whether the graph of each quadratic function
opens upward or downward.
12.
11.
UP or DOWN
UP or DOWN
14.
13.
UP or DOWN
UP or DOWN
April 01, 2014
Vertex:
The highest or lowest point on a parabola is the
vertex.
o
If a parabola opens upward, the vertex is the lowest point.
- Thus, the y-value of the vertex is the
__________________ value of the function.
o
If a parabola opens downward, the vertex is the highest point.
- Thus, the y-value of the vertex is the
__________________ value of the function.
April 01, 2014
Identify the vertex of the parabolas we graphed in
problems 9 & 10. Then give the minimum or maximum
value of the function.
10.
9.
Vertex:
Vertex:
Max/Min Value:
Max/Min Value:
April 01, 2014
Domain and Range:
Unless a specific domain is given, you may assume
that the domain of a quadratic function isall the real
numbers. You can find range by looking at the
graph.
Find the domain and range .
Step 1: Determine the direction of the
quadratic function.
Find the minimum/maximum value.
Step 2: Find the domain and range.
Domain: _______________
Range: ________________