Name: _________________________________________________________
Traits of Parabolas
You have learned a lot about quadratic equations (parabolas) over the past few weeks. Today we
will continue to add to the knowledge you have gained. Use your team to make sure that each
part of this assignment makes sense.
I. We have worked on finding intercepts in t-tables and graphs. We can use these same ideas
to find the vertex. Find the x- intercepts (also known as zeros and roots), y-intercepts and the
vertex in each of these situations.
Using a T-Table
Using a Graph
y = x2 + 4x +3
y = x2 - 4x - 5
x
y
-4
3
-3
0
-2
-1
0
3
1
8
(___,___)
I know that (_____, ______) is the vertex
because:
The x-intercepts are:_____ & _______
The y-intercept is:_________
(___,___)
The x-intercepts are:_____ & _______
The y-intercept is:_________
The general form for all quadratics is:
y=a x 2b xc
In the general form, a term is called the _____________________________. This is
because it is the number in front of the variable with the highest degree.
The a term also tells us if the parabola _____________________________ based on the
sign in front of it, while the value of the a identifies the factor of ____________________.
y = x2 - x - 6
Direction
Circle one:
Opens Up
Vertex
Opens Down
Identify a, b, &, c.
a = _____
How do you know?
b = ______ c = _______
Find Axis of Symmetry. Use the formula:
This is a (circle one):
Minimum
Maximum
x=
−b
=
2a
Substitute the value of x into the quadratic and
write the equation below.
X-Intercepts
y = _______________________
Factor the quadratic:
Solve for y.
0 = (_________)(_________)
Apply the zero product property and determine
the value(s) of x:
The vertex is: (_____,_____)
x = __________ or ____________
Sketch the graph
First plot & label the vertex.
Vertex: ______________
Next plot & label the xintercepts.
x-intercepts: _____ & _____
Then plot & label the y-intercept
- it is always the constant term.
y-intercept: __________
Finally draw the parabola!
My Quadratic: ______________________________
Direction
Circle one:
Opens Up
Vertex
Opens Down
Identify a, b, &, c.
a = _____
How do you know?
b = ______ c = _______
Find Axis of Symmetry. Use the formula:
This is a (circle one):
Minimum
Maximum
x=
−b
=
2a
Substitute the value of x into the quadratic and
write the equation below.
X-Intercepts
y = _______________________
Factor the quadratic:
Solve for y.
0 = (_________)(_________)
Apply the zero product property and determine
the value(s) of x:
The vertex is: (_____,_____)
x = __________ or ____________
Sketch the graph
First plot & label the vertex.
Vertex: ______________
Next plot & label the xintercepts.
x-intercepts: _____ & _____
Then plot & label the y-intercept
- it is always the constant term.
y-intercept: __________
Finally draw the parabola!