Here is where you will learn battle techniques to fight over the Arithmetic Plane against Mr. Linear. The graphing plane! But not just any graphing, make sure its quadratic and not linear so you are not a slave to the despicable villain. Hopefully you have graphed before because we're not reviewing this stuff, but one bit of vocabulary: parabola, a graph shape that looks like a "U" or an upside down "U". When a quadratic equation is graphed, it makes a parabola.
If presented with a standard, let's say factorable, equation like this, x² + 5x + 6 = 0, or x² + 5x + 6 = y for our purposes. The simplest way to graph is to do the following:
1. Find the vertex, the highest or lowest point of the graph. This is done with the formula x = -b/2a. After plugging this in you will have the x coordinate of the vertex and now all you have to do is plug your value into the equation, solve for y, and plot your vertex!
2. The second step is very simple. All you have to do is look at the a term and see if its positive or negative. If a is positive you know your parabola will open upwards, while a negative a would mean the graph opens downward. And if the graph opens up you know your vertex is the lowest point while a graph going down has the vertex as the highest point.
3. Now use the chart method of graphing and select three points as x, solve for y, and plot the points, make all the x values greater than the x of the vertex.
4. Draw a dotted line along the axis of symmetry, the x line that passes up and down the parabola and through the vertex. Now put a point of the graph opposite the axis of symmetry to all your previous points.
5. Here it is. The big step. Fudge the parabola. That's right, draw a line through all your points as you think the graph would look. Put arrows at the ends of the parabola to represent the fact that the lines go forever.
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