1. Bell Ringer  1. How many roots do quadratic functions have?  2. What kind of root is it when the quadratic function touches the x-axis and “bounces back”?  3. If a quadratic function does not cross the x-axis, what are the nature of it’s roots?

2. Graphing in the Complex Plane Graphing Quadratics in the Coordinate Plane Monday, September 28, 2015

3. Graphing  The Coordinate Plane  The Complex Plane

4. Remember Quadratics?

5. Remember…  Standard form of a quadratic is ax 2 + bx + c  The Fundamental Theorem of Algebra says that every polynomial has roots equivalent to its degree. Therefore, all quadratics have 2 roots.  Roots = Solutions = Zeros = x-intercepts  So, what happens when the Quadratic does not cross the real number line?

6. If the quadratic doesn’t cross the real number line (x-axis)…  Then your two roots are imaginary (aka complex).

7. Time to Practice!  Complete notes: The Complex Plane  Homework: Complex Bumper Stickers