Question

How do you graph $y = 2{x^2} - 8x - 1$ by plotting points?

Answer 1

A graph of a function f is the set of ordered pairs; the equation of the graph is generally represented as $y = f\left( x \right)$ , 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 $y = f\left( x \right)$, 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 equation of function $y = 2{x^2} - 8x - 1$. Let us substitute the value of x has $- 1$, $0$, $1$ and $2$.
Now we consider the value of x as $- 1$, the value of y is
$\Rightarrow y = 2{\left( { - 1} \right)^2} - 8\left( { - 1} \right) - 1$
$\Rightarrow y = 2\left( 1 \right) + 8 - 1$
$\Rightarrow y = 9$
Now we consider the value of x as $0$, the value of y is
$\Rightarrow y = 2{\left( 0 \right)^2} - 8\left( 0 \right) - 1$
$\Rightarrow y = - 1$
Now we consider the value of x as $1$, the value of y is
$\Rightarrow y = 2{\left( 1 \right)^2} - 8\left( 1 \right) - 1$
$\Rightarrow y = - 7$
Now we consider the value of x as $2$, the value of y is
$\Rightarrow y = 2{\left( 2 \right)^2} - 8\left( 2 \right) - 1$
$\Rightarrow y = 2\left( 4 \right) - 16 - 1$
$\Rightarrow y = - 9$
Now we draw a table for these values we have

x	$- 1$	$0$	$1$	$2$
y	$9$	$- 1$	$- 7$	$- 9$

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.