Properties of Quadratics

Topic A Key Information:

• Properties of Quadratics
• Graphing and Understanding Quadratics

 

An equation is quadratic if an only if the power of x is two and the power of y is one. It will always form a parabola. Factoring finds where the graph crosses the x-axis, if it crosses the x-axis.

Here is the quadratic equation in the generic format:

y=ax² + bx +c

If you were to input a series of values for the x coordinate or “x,” and plot your resulting sets of coordinates, your image would result in a parabola.

For example the quadratic function  f(x)=x²+x+1 results in a graph like this:

The graph results in a parabola because both positive and negative values of x are used.