17 A – Cubic Polynomials

3: Graphing Cubics from General Form

The Zeros and Maximum/Minimum Turning

Points of a Polynomial• The zeros of any polynomial are the values of x which

make y have a value of zero.– Also known as the x-intercepts.– The zeros of y = a(x – α)(x – β)(x – γ) are α, β, and

γ.• The maximum and minimum

turning points of a graph can easily be found using a graphing calculator.

Graphing Cubics from General Form

• Consider f(x) = 3x3 – 14x2 + 5x + 2.1. Graph the function on a graphing calculator.2. Find the zeros (`$2).3. Find the y-intercept (use $ or substitute x = 0

into the equation and solve).4. Find the minimum and maximum turning points

(`$3 for min, `$4 for max).

You can use this information to sketch an accurate graph of the function!