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Grade 21 Algebra II
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Quadratic Equations and Functions -Modeling Data with Quadratic Functions
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Question: Determine which of the graphs represent a quadratic function.
A ) Graph 1 and Graph 4
B ) Graph 1 only
C ) Graph 1 and Graph 3
D ) Graph 4 only
Steps to derive
1
The graph of a quadratic function is a parabola.
2
Graph-1 is a parabola.
3
Graph-2 is a straight line.
4
Graph-3 shows the graph of an absolute function.
5
Let’s check Graph-4.
6
The points that lie on graph 4 are: (- 2, 2), (- 1, 3.5) and (0, 4)
7
Substitute each point in
y
=
a
x
2
+
b
x
+
c
, - - - - (1) the standard form of equation of a parabola.
8
4 =
a
(0)
2
+
b
(0) +
c
9
⇒
c
= 4
[Substitute the values.]
10
4
a
- 2
b
+
c
= 2 and
a
-
b
+
c
= 3.5
[Substitute the values.]
11
c
= 4 reduces the two new equations to: 4
a
- 2
b
= - 2 - - - - (2) and
a
-
b
= - 0.5 - - - - (3)
12
Solve (2) and (3) to get the values of
a
and
b
.
13
a
= -
1
2
and
b
= 0
14
So,
y
= - (
1
2
)
x
2
+ 0
x
+ 4
[Substitute the values.]
15
⇒
y
= - (
1
2
)
x
2
+ 4, which is an equation of a parabola.
16
So the graph 1 and graph 4 represent quadratic functions.
Hence the right answer is Option A
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