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 .