Find Equation for a Cubic Function with Zeros -2 and 3 and Y-Intercept 9

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To find the equation of a cubic function with given zeros -2 (with order 2) and 3, and a y-intercept of 9, start by expressing the function as f(x) = k(x + 2)²(x - 3). The y-intercept condition requires that f(0) = 9, leading to the equation k(2)²(-3) = 9. Solving for k gives k = -3/4, resulting in the final equation y = -3/4(x + 2)²(x - 3). This method effectively utilizes the properties of cubic functions to derive the desired equation.
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Homework Statement


When you are given the type of function, the roots and the zeros, how do you find the equation?
Information given was:
a cubic function with zeros -2 (order 2) and 3 and y-intercept 9

Homework Equations


N/A


The Attempt at a Solution


since zeros are -2 and 3, x+2 and x-3
i called this equation f(x)
since y-intercept if 9, f(0)=9

The correct answer is y= -3/4(x+2)^2(x-3)
 
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