Question

How do you graph \[y = \dfrac{1}{4}{x^2}\] ?

Answer 1

Hint: A graph of a function f is the set of ordered pairs; the equation of graph is generally represented as \[y = f(x)\] , where x and f(x) are real numbers. We substitute the value of x and we determine the value of y and then we mark the points in the graph and we join the points.

Complete step by step solution:
Here in this question, we have to plot the graph for the given function. A graph of a function is a set of ordered pairs and it is represented as \[y = f(x)\] , where x and f(x) are real numbers. These pairs are in the form of cartesian form and the graph is the two-dimensional graph.
First, we have to find the value of y by using the graph equation \[y = \dfrac{1}{4}{x^2}\] . Let us substitute the value of x has -6, -4, -2, 0, 2, 4, and 6. Here we have chosen the points which are multiples of two, because in the equation of a graph we have a fraction and the denominator contains 4 and we have \[{x^2}\] in the numerator.
Now we consider the value of x as -6, the value of y is
 \[
   \Rightarrow y = \left( {\dfrac{1}{4}} \right){( - 6)^2} \\
   \Rightarrow y = \dfrac{1}{4} \times 36 \\
   \Rightarrow y = 9 \;
 \]
Now we consider the value of x as -4, the value of y is
 \[
   \Rightarrow y = \left( {\dfrac{1}{4}} \right){( - 4)^2} \\
   \Rightarrow y = \dfrac{1}{4} \times 16 \\
   \Rightarrow y = 4 \;
 \]
Now we consider the value of x as -2, the value of y is
 \[
   \Rightarrow y = \left( {\dfrac{1}{4}} \right){( - 2)^2} \\
   \Rightarrow y = \dfrac{1}{4} \times 4 \\
   \Rightarrow y = 1 \;
 \]
Now we consider the value of x as 0, the value of y is
 \[
   \Rightarrow y = \left( {\dfrac{1}{4}} \right){(0)^2} \\
   \Rightarrow y = \dfrac{1}{4} \times 0 \\
   \Rightarrow y = 0 \;
 \]
Now we consider the value of x as 2, the value of y is
 \[
   \Rightarrow y = \left( {\dfrac{1}{4}} \right){(2)^2} \\
   \Rightarrow y = \dfrac{1}{4} \times 4 \\
   \Rightarrow y = 1 \;
 \]
Now we consider the value of x as 4, the value of y is
 \[
   \Rightarrow y = \left( {\dfrac{1}{4}} \right){(4)^2} \\
   \Rightarrow y = \dfrac{1}{4} \times 16 \\
   \Rightarrow y = 4 \;
 \]
Now we consider the value of x as 6, the value of y is
 \[
   \Rightarrow y = \left( {\dfrac{1}{4}} \right){(6)^2} \\
   \Rightarrow y = \dfrac{1}{4} \times 36 \\
   \Rightarrow y = 9 \;
 \]
Now we draw a table for these values we have

x	-6	-4	-2	0	2	4	6
y	9	4	1	0	1	4	9

The graph plotted for this point is represented below:

Note: The graph is plotted x-axis versus y axis. The graph is two dimensional. By the equation of a graph, we can plot the graph by assuming the value of x. We can’t assume the value of y. because the value of y depends on the value of x. Hence, we have plotted the graph.