Name _______________________________________ Date __________________ Class __________________
Characteristics of Quadratic Functions
Fill in the blanks and the y column of the chart.
Quadratic functions are written in the
form y = ax2 + bx + c, where a ≠ 0.
The graph of a quadratic
function is a ___________
1 2
x +3
2
a =______ b = _____ and c = _____
y=−
vertex: ( ,
You can
create a
table of
values to
graph a
quadratic
function.
x
y
−4
−2
0
2
4
The graph of
1
y = − x2 + 3
2
opens
________
because
________
Recall that
the domain
is the set of
x-values and
the range is
the set of
y-values for
a function.
); max or min
D: ______
R: ________
Complete the following.
1. Identify the values of a, b, and c in the quadratic function y = 3x2 − 5 x + 2.
________________________________________________________________________________________
2. Does the graph of the function y = 3x2 − 5 x + 2 open upward or downward?
________________________________________________________________________________________
3. Identify the domain and range for a function whose graph opens upward with vertex (0, −5).
________________________________________________________________________________________
Answer the following about the function y = 2x2.
4. Create a table of values for the function.
x
5. Graph the function.
6.What is the vertex of the graph?
___________________________
7. Does the graph open upward or
or downward? Why?
__________________________________
y
Name _______________________________________ Date __________________ Class __________________
Tell whether each function is quadratic. Explain.
1. (0, 6), (1, 12), (2, 20), (3, 30)
2. 3x + 2y = 8
Use a table of values to graph each quadratic function.
1
3. y = − x 2
4. y = 2x2 − 3
2
x
y
x
y
Tell whether the graph of each quadratic function opens upward or
downward. Explain.
5. y = −3x2 + 5
6. −x2 + y = 8
________________________________________
________________________________________
For each parabola, a) identify the vertex; b) give the minimum or
maximum value of the function; c) find the domain and range.
8.
7.
a. _____________________________________
a. _____________________________________
b. _____________________________________
b. _____________________________________
c. _____________________________________
c. _____________________________________
Homework: p. 615 1, 22 – 44, 53 – 60
Name _______________________________________ Date __________________ Class __________________