1. Identify the values of a, b, and c.

2. Write the two real roots.

3. We can write our result as two equations equal to 0. Only a mechanical move.

4. This result shows that not all quadratic equations can be graphed using real roots. Sometimes it is necessary to make a table of values.

Making a table of values should not be a guessing gave. We need to make sure we use the axis of symmetry to determine what values to use for the x-coordinates. The axis of symmetry gives us the location where in the coordinate plane to graph our parabola. Below is I started with x = 0 only because I knew in advance the x-coordinate 0 was mighty close to the axis of symmetry of this particular graph.

Simple computations. You must know how to do this well. Practice on your own.

The x-coordinate of the vertex is 1. The y-coordinate is -7. We know these values from our table. The axis of symmetry is not graphed here, you must use your imagination. The formula to find the x-coordinate of the vertex was used here. This confirms that our table of values is correct. In the future we must compute the x-coordinate of the vertex first to help us guide our table of values. Notice that this parabola has a minimum value and since a is positive, it opens upwards.