ALGEBRA II HONORS/GIFTED - SECTION 10-6 @ HIGHER DEGREE FUNCTIONS AS MATHEMATICAL MODELS 1

ALGEBRA II HONORS/GIFTED - SECTION 10-6 1) You must know 2 points to find the equation for a line and 3 points to find the equation for a quadratic. How many points do you think you need to know to find the equation for a cubic function? ANSWER : 4 points 2

Standard Form for a Cubic Equation y = ax3 + bx2 + cx + d 2) Find the particular equation of the cubic function containing the point (1, 3), (2, 4), (3, 25) and (4, 78). SOLUTION: 3 = a(1)3 + b(1)2 + c(1) + d 4 = a(2)3 + b(2)2 + c(2) + d 25 = a(3)3 + b(3)2 + c(3) + d 78 = a(4)3 + b(4)2 + c(4) + d

ALGEBRA II HONORS/GIFTED - SECTION 10-6 3 = a + b + c + d 4 = 8a + 4b + 2c + d 25 = 27a + 9b + 3c + d 78 = 64a + 16b + 4c + d Use the MATRIX menu of your graphing calculator to determine the solution. A-1B 4

The solution is : y = 2x3 – 2x2 – 7x + 10 3) Find the particular equation for the cubic function containing (-5, -80), (-3, 0), (1, 16), (4, 91). SOLUTION: y = x3 + x2 - x + 15

This is the last lesson of the year. So, it can’t be long until…..