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Write a cubic function whose graph is shown (2,0),(-1,0),(0,6),(3,0)

User NaderNader
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The cubic function with zeros at (2,0), (-1,0), and (3,0) and a point on the graph at (0,6) is f(x) = (x - 2)(x + 1)(x - 3).

To write a cubic function that has zeros at (2,0), (-1,0), and (3,0), we use the fact that a cubic function has the form:

f(x) = a(x - r1)(x - r2)(x - r3)

where 'a' is a constant and r1, r2, r3 are the roots of the equation.

Given the roots 2, -1, and 3, the function takes the form:

f(x) = a(x - 2)(x + 1)(x - 3)

By using the point (0,6), which is not a root but a point on the graph, we can find the value of 'a'.

f(0) = 6 = a(0 - 2)(0 + 1)(0 - 3)

6 = a(-2)(1)(-3)

6 = 6a

a = 1

Therefore, the cubic function is:

f(x) = (x - 2)(x + 1)(x - 3)

User Custom Bonbons
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