Question

How do I graph the quadratic equation \[y = - 3{x^2}\] ?

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 answer:
Now consider the given equation \[y = - 3{x^2}\]. 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 \[y = - 3{x^2}\]. Let us substitute the value of x has -2, -1, 0, 1 and 2.
Now we consider the value of x as -2, the value of y is
\[
   \Rightarrow y = - 3{( - 2)^2} \\
   \Rightarrow y = - 3(4) \\
   \Rightarrow y = - 12 \;
 \]
Now we consider the value of x as -1, the value of y is
\[
   \Rightarrow y = - 3{( - 1)^2} \\
   \Rightarrow y = - 3(1) \\
   \Rightarrow y = - 3 \;
 \]
Now we consider the value of x as 0, the value of y is
\[
   \Rightarrow y = - 3{(0)^2} \\
   \Rightarrow y = 0 \;
 \]
Now we consider the value of x as 1, the value of y is
\[
   \Rightarrow y = - 3{(1)^2} \\
   \Rightarrow y = - 3(1) \\
   \Rightarrow y = - 3 \;
 \]
Now we consider the value of x as 2, the value of y is
\[
   \Rightarrow y = - 3{(2)^2} \\
   \Rightarrow y = - 3(4) \\
   \Rightarrow y = - 12 \;
 \]
Now we draw a table for these values we have

X	-2	-1	0	1	2
y	-12	-3	0	-3	-12

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.