NAME_______________________________ DATE___________________ PERIOD_______
GRAPH THE FOLLOWING QUADRATICS.
Give:
b
, plug in to find y)
2a
b
Axis of symmetry : x 
2a
a. Vertex (
b.
c.
d.
e.
f.
Graph:
a.
b.
c.
d.
x y table with 2 points other than vertex close to ONE side of the axis of symmetry
Domain
Range
Root(s)
Vertex
Axis of symmetry (use a dashed line)
2 points from your x y table
2 mirror points (same y value on the other side of axis of symmetry)
e. Connect points to make a smooth U putting arrows at the end
1. y = x2
a. Vertex: (
,
)
b. Axis of symmetry:
c. x y table
x
d. Domain:{ 
e. Range: { 
y
}
}
f. Root(s):
2. y = x2 + 2
a. Vertex: (
,
)
b. Axis of symmetry: x =
c. x y table
x
d. Domain:{ 
e. Range: { 
Compare this graph to y = x2
What's similar?
What's different?
y
}
}
f. Root(s):
3. y = 2x2
a. Vertex: (
,
)
b. Axis of symmetry: x =
c. x y table
x
d. Domain:{ 
e. Range: { 
Compare this graph to y = x2
What's similar?
What's different?
y
}
}
f. Root(s):
4. y = 2x2 + 2
a. Vertex: (
,
)
b. Axis of symmetry: x =
c. x y table
x
d. Domain:{ 
e. Range: { 
Compare this graph to y = 2x2
What's similar?
What's different?
y
}
}
f. Root(s):
5. y = ⅓ x2
a. Vertex: (
,
)
b. Axis of symmetry: x =
c. x y table
x
d. Domain:{ 
e. Range: { 
Compare this graph to y = x2
What's similar?
What's different?
y
}
}
f. Root(s):
6. y = -x2
a. Vertex: (
,
)
b. Axis of symmetry: x =
c. x y table
x
d. Domain:{ 
e. Range: { 
Compare this graph to y = x2
What's similar?
What's different?
y
}
}
f. Root(s):
7. y = x2 - 4x
a. Vertex: (
,
)
b. Axis of symmetry: x =
c. x y table
x
d. Domain:{ 
e. Range: { 
Compare this graph to y = x2
What's similar?
What's different?
y
}
}
f. Root(s):
8. y = x2 - 4x + 8
a. Vertex: (
,
)
b. Axis of symmetry: x =
c. x y table
x
d. Domain:{ 
e. Range: { 
y
}
}
Compare this graph to y = x2 - 4x
What's similar?
What's different?
What is the equation in Vertex Form?
f. Root(s):
9. y = -2x2 + 4x - 8
a. Vertex: (
,
)
b. Axis of symmetry: x =
c. x y table
x
d. Domain:{ 
e. Range: { 
y
}
}
Compare this graph to all the previous graphs.
What's similar?
What's different?
What is the equation in Vertex Form?
f. Root(s):
10. y  ( x  3)2  2
a. Vertex: (
,
)
b. Axis of symmetry: x =
c. x y table
x
d. Domain:{ 
e. Range: { 
h=
k=
y
}
}
f. Root(s):
What effect did h have on the parabola?
What effect did k have on the parabola?
What is the equation in Standard Form?
Does it have a minimum or maximum? Explain.
1
11. y  ( x  4) 2  3
2
d. Vertex: (
,
)
e. Axis of symmetry: x =
f. x y table
x
f. Domain:{ 
g. Range: { 
h=
k=
y
}
}
f. Root(s):
What effect did h have on the parabola?
What effect did k have on the parabola?
What is the equation in Standard Form?
Does it have a minimum or maximum? Explain.
12. Create your own graph having the following parameters:
a. Select a vertex in the 4th quadrant: (
,
)
Axis of symmetry: x =
b. Make the a coefficient a positive whole number.
c. Give the equation in Vertex Form.
d. Graph.
e. Circle the roots on the graph and list them. If they are not integers,
tell the consecutive integers that they lie between.
x y table
x
f. Domain:{ 
g. Range: { 
y
}
}
g. Root(s):
What is the equation in Standard Form?
Does it have a minimum or maximum? Explain.
13. Begin with the parent graph equation and transform it in Vertex
Form for the following parameters (do not graph, but use your graphing
calculator to verify):
a.
Reflect (flip) it over the x-axis.
b.
Translate (slide) it up 4 places.
c.
Translate it to the left 3 places.
d.
Translate it both down 5 and right 7 places.
e.
Dilate it (widen or narrow it) by a scale factor of 2.
f.
Dilate it by a scale factor of ¾ .
g.
Reflect it over the x-axis, dilate it by a factor of 3, and translate up
1 place and right 2 places.
h.
Why aren’t we rotating (turning) the graph right or left right now?
ANSWER THE FOLLOWING SUMMARY QUESTIONS
The Standard Form of a quadratic is:
The Vertex Form of a quadratic is:
Assume the quadratic is in Standard Form and answer the following:
The formula for the x-value of the vertex is:
Once you have the x-value of the vertex, what else do you know
immediately?
How do you find the y-value of the vertex?
Why should you stay as close as possible to the AOS when finding
two additional points in your x-y table?
What is the relationship between the vertex and the range?
How do you change Vertex Form to Standard Form?
How do you think you would go about changing the Standard Form to
Vertex Form?