Question

How do you graph $f\left( x \right)={{x}^{2}}-5x+9$ using a table?

Answer 1

Hint: We will construct a table of two rows with the first row containing the values of the $x-$coordinates and the second row contains the values of $y-$coordinates. We can take as many points as required.

Complete step by step answer:
We are asked to graph the given function $f\left( x \right)={{x}^{2}}-5x+9$ using a table.
We will draw a table with two rows.
We know that we need to find the points through which the curve passes.
We will draw a table with two rows. In the first row, we will accommodate some $x-$coordinates in each column. And in the second row, we will accommodate the corresponding $y-$coordinates. So, we can say that the number of columns of the table is equal to the number of points we need to draw the graph.
Let us choose the $x-$coordinates, $0,1,2,3,4,5.$
Now, to find the corresponding $y-$coordinates, we will apply the $x-$coordinates in the function.
So, when $x=0,$ the function value will be $f\left( 0 \right)=9.$
Similarly, we will get when $x=1,$ the value of the function is $f\left( 1 \right)=5.$
We can find the $y-$coordinate corresponding to the $x-$coordinate by $f\left( 2 \right)=3.$
And when we apply $x=3,$ we will get the corresponding function value as $f\left( 3 \right)=3.$
Now, let us take $x=4,$ then we will get $f\left( 4 \right)=5.$
Finally, let us take $x=5.$ We will get $f\left( 5 \right)=9.$
So, we will get the following table by inserting the above values:

x	0	1	2	3	4	5
Y=f(x)	9	5	3	3	5	9

Now, we can draw the graph by marking the points in the table.
We will get,

Note: In this problem, we have selected points from the positive axis. We can also take negative $x-$coordinates and find the corresponding $y-$coordinates. For example, when we take $x=-1,$ we will get $f\left( -1 \right)=15.$ And when we take $x=-2,$ we will get $f\left( -2 \right)=23.$ We can also include these values in the table.