Fill the table below with the appropriate coordinates and graph the quadratic equation, y = -x2 -2x +3.
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:
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
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:
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:
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:
By repeating the same step for the rest of the x-coordinates, we get the following:
Hence, we can plot the points as shown:
By drawing a curve to join these points together, we get the graph of y = -x2 -2x +3.
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