Answer:
Explanation:
Given the Equation :
y
=
f
(
x
)
=
4
x
2
A Quadratic Equation takes the form:
y
=
a
x
2
+
b
x
+
c
Graph of a quadratic function forms a Parabola.
The coefficient of the
x
2
term (a) makes the parabola wider or narrow.
If the coefficient of the
x
2
,
term (a) is negative. then the parabola opens down.
The term Vertex is used to identify the Turning Point of a parabola.
It can be maximum point or minimum point, depending on the sign of the coefficient of the
x
2
term.
Step 1 :
Create a data table as shown below:
enter image source here
Notice that the column E contains values for
x
2
y
=
x
2
is the Parent Function for a quadratic equation.
The graph of
y
=
x
2
is useful in understanding the behavior of the function given
y
=
4
x
2
.
Since, the sign of the
x
2
term is positive, the parabola opens up and we have a Minimum point at the Vertex.
Step 2 :
Plot the Points from the data table to draw graphs.
Graphs of
y
=
x
2
, the parent function and
y
=
4
x
2
are:
enter image source here
Observe that the coefficient of the
x
2
, which is
4
, makes the parabola of
y
=
4
x
2
,
narrow.
Hope it helps.
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