This week in precalc I learned that the completing the square form of an equation is the same as a general quadratic graphing equation, so if I complete the square I can easily fill in a graph.

If an equation is in standard factoring form, I can simply convert that to a completing the square form as well, allowing me to easily solve graphs so long as I can change the equation to what I need it to be.

Additionally, if an equation is already factored, I simply expand it, and continue on until I have completed the square.

Essentially, all I need to do is complete the steps to convert it to the right form, and the graph becomes easy to solve.

The form I need to find looks like this:

This week in precalc, I learned about the standard form of quadratic equations and how every piece determines a part of its graph. It is an easy and effective way to graph any quadratic equation.

The standard form looks like this:

To start, the will modify the width of the parabola, either expanding or compressing it. If , the parabola will look like a regular parabola. However, if , it will expand and look thinner, whereas if , it will compress and look wider.

Next, there is the , which determines the x value of the vertex. As the value of increases, the vertex moves right, and as it decreases, it moves left.

Finally, you have , which determines the y value of the vertex. If the value of increases, then the vertex will move upwards, and if it decreases, it moves downwards.

Additionally, if the right side of the equation is negative, the parabola will open down and have a maximum point. You can also plug in various points of the graph into the equation at and .