Equation determine Pre Calc

Question

A) Determine the equation of the function with zeros 2(order 3) and -1/2 (order 1) that passes through a y-intercept of -4.

B) Create a sketch of this curve

Answer 1

x = 2, 2, 2, -1/2

Use the zeros to get:

y = (x - 2)³ (x + 1/2)

Multiply factors to get:

y = x⁴ - (11/2)x³ + 9x² - 2x - 4

Check the y-intercept:

y(0) = (0)⁴ - (11/2)(0)³ + 9(0)² - 2(0) - 4 = -4

The above function already has a y-intercept of (0,-4) so there is no need to alter it. Your final equation is:

y = x⁴ - (11/2)x³ + 9x² - 2x - 4