Graphs of Quadratics
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School
The University of Tennessee, Knoxville *
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Course
ARCH-211
Subject
Mathematics
Date
Jan 9, 2024
Type
docx
Pages
3
Uploaded by shivamp2001
M119 GAO Graphs of Quadratics
Name:
UT Email Address:
Replace
your name
in the file name with your
UT email address
.
(Click in the upper left corner of the document to the right of the Doc icon.)
For each quadratic function, do the following:
a.
Find the vertex.
(Show your work in the “Work for parts a & c Here” box.)
b.
Find the equation for the axis of symmetry.
c.
Find the
x
-intercepts.
(Show your work in the “Work for parts a & c Here” box.)
d.
Graph the function.
Sketch each graph by hand.
(
Hint:
parabolas should be “uv”-shaped.
No vertical sides.
No
pointy vertex.)
Then, insert a picture of your graph into the appropriate answer box in the “Answers Here” table.
Please make sure that your graph is an appropriate size.
Please make sure to draw and label your axes clearly.
If you need a refresher on how to insert images into your Google doc, review
Inserting Images of Written
Work and Graphs in Google Docs
.
There is information there about using the
Empty Graph
template as
well.
You are encouraged to use a straightedge to draw your axes (if you choose not to use the Empty Graph
template) and your lines.
Computer generated graphs will not be accepted.
You must draw them yourself either
by hand or using the drawing tool within Google docs.
(Click in the appropriate answer box, then choose Insert
-> Drawing -> New).
e.
Indicate whether the vertex is a relative maximum or a relative minimum. (Just write max or min in the blank.)
f.
List the interval where the function is increasing (interval notation).
g.
List the interval where the function is decreasing (interval notation).
h.
Find the domain (interval notation).
i.
Find the range (interval notation).
j.
Write the equation for the function in standard form:
x
−
h
¿
2
+
k
f
(
x
)=
a
¿
. (
Hint: you should be able to figure out
a
,
h
, and
k
by examining the transformations of the graph - think HRV.)
1.
Work for parts a & c Here (no images of written work):
−
4
2
(−
1
)
=
2
x
=
2
y
=−
2
❑
❑
2
+
4
(
2
)=
4
0
=−
x
❑
2
+
4
x
−
x
(
x
−
4
)
x
=
0
, x
=
4
Answers Here:
a.
List the vertex. (ordered pair)
(2,4)
b.
List the equation for the axis of symmetry.
x
=
2
c.
List the
x
-intercept(s) as ordered pairs.
(0,0),(4,0)
d.
Graph the function.
e.
Is the vertex a relative max or min?
Max
f.
List the interval where the function is
increasing (interval notation).
(−
∞ ,
2
)
g.
List the interval where the function is
decreasing (interval notation).
(2,
∞
¿
h.
List the domain (interval notation).
(−
∞ ,∞
)
i.
List the range (interval notation).
¿
j.
Write the equation for the function in
standard form:
x
−
h
¿
2
+
k
f
(
x
)=
a
¿
f
(
x
)=−(
x
−
2
)
❑
2
+
4
2.
Work for parts a & c Here:
−
2
2
(
1
)
=−
1
y
=(−
1
)
❑
2
+
2
(−
1
)−
8
=−
9
(−
1
,
−
9
)
0
=
x
❑
2
+
2
x
−
8
x
+
4
¿
=
0
¿
(
x
−
2
)
¿
x
=
2
,x
=−
4
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