Create the equation of a cubic in standard form that has a double zero at -2, another zero at 4, and a y-intercept of 16,

f(x) = x³ - 3x - 4

Step-by-step explanation:

Given that x = - 2 has multiplicity 2 and x = 4 are zeros then

(x + 2)² and (x - 4) are the factors of the polynomial and the polynomial is the product of the factors, thus

f(x) = a(x + 2)²(x - 4) ← a is a multiplier

To find a substitute (0, 16) into the equation

16 = a(4)(16), thus

64a = 16

a = =

f(x) = (x + 2)²(x - 4) ← expand factors

    = (x² + 4x + 4)(x - 4)

    = (x³ + 4x² + 4x - 4x² - 16x - 16)

    = (x³- 12x - 16)

   = x³ - 3x - 4

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.