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zlopas [31]
3 years ago
10

The function f(x) is a cubic function and the zeros of f(x) are -3, -2, and 1. The y-intercept of f(x) is -24. Write the equatio

n of the cubic polynomial in standard form.
Mathematics
1 answer:
Serga [27]3 years ago
7 0

Answer:

f(x) = 4x³+16x²+4x-24

Step-by-step explanation:

Factors are (x+3)(x+2)(x-1)

(x+3)(x²+2x-x-2)

(x+3)(x²+x-2)

x³+x²-2x+3x²+3x-6

x³+4x²+x-6

This could have been the function but the intetcept is 6 here.

So we'll take a miltiple of this one such that the intercept becomes-24

-24/-6 = 4

That multiple is 4

f(x) = 4(x³+4x²+x-6)

f(x) = 4x³+16x²+4x-24

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\bf \textit{using the pythagorean theorem}&#10;\\\\&#10;c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b&#10;\qquad &#10;\begin{cases}&#10;c=hypotenuse\\&#10;a=adjacent\\&#10;b=opposite\\&#10;\end{cases}&#10;\\\\\\&#10;\sqrt{41^2-(-9)^2}=b\implies \sqrt{1681-81}=b\\\\\\ \sqrt{1600}=b\implies 40=b\\\\&#10;-------------------------------

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