Step 1

Before we start graphing, we need to fill the table with the appropriate coordinates. To do so, first, we have to get the x-coordinates by using the formula for the x-coordinate of the vertex:

Step 2

To use the formula, we need to get the values of a and b. We can do so by comparing the given quadratic equation with the general quadratic equation as shown below:

By comparing, we have a = -1, b = -2 and c = 3

Step 3

Now, we can substitute the equation with a = -1 and b = -2. By doing so, we can solve for x.

Hence, we can fill the table with x = -1 as shown below:

Step 4

With this, we know that the vertex has the x-coordinate of 1. Since the vertex lies on the center of the graph, we can choose the rest x-coordinates using x = -1 as a reference.

Hence, we can choose three x-coordinates smaller than -1 (-2, -3, -4) and three x-coordinates greater than -1 (0, 1, 2). Therefore, the table becomes:

Step 5

We can start calculating the y-coordinates. For x=-4, we can calculate for the y-coordinate by substituting x with -4 into the equation:

Hence, we can fill the table as shown:

Step 6

By repeating the same step for the rest of the x-coordinates, we get the following:

Step 7

Hence, we can plot the points as shown:

Step 8

By drawing a curve to join these points together, we get the graph of y = -x² -2x +3.