Lesson: Extension Cubic Functions and Equations Obj: The student will be able to 1) Recognize and graph cubic functions 2) Solve cubic equations HWK: p 603 1-9 all Vocab: 1) cubic function – a function that can be written in the form f(x) = ax³ + bx² + cx + d where a ≠ 0 2) cubic equation – an equation that can be written in the form ax³ + bx² + cx + d = 0 where a ≠ 0

Parent function f(x) = x³ Graph this function From this graph we can see:

Graph the function. Identify the intercepts and give the domain and the range. Ex 1) f(x) = -2x³ + 3x² + x - 4

Ex 2) f(x) = (x – 1)³

Ex 3) f(x) = 2x³ - 12x² + 18x

Ex 4) f(x) = -2x³ + 3x² + x – 4 Ex 5) f(x) = (x – 1)³ Find the solutions of each function from the graphs using the graphs in Examples 1, 2, and 3. Check your answer. Ex 4) f(x) = -2x³ + 3x² + x – 4 Ex 5) f(x) = (x – 1)³

Ex 6) f(x) = 2x³ - 12x² + 18x

Solve each equation algebraically. Check your answer. Ex 7) (x + 2)³ = 64 Ex 8) 4x³ - 12x² + 4x = 0

Ex 9) x³ + 3x² = 10x