17 A – Cubic Polynomials 3: Graphing Cubics from General Form.

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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) = 3x 3 – 14x 2 + 5x 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!