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Irina-Kira [14]
2 years ago
11

Suppose the graph of a cubic polynomial function has the same zeroes and passes through the coordinate (0, –5). Describe the ste

ps for writing the equation of this cubic polynomial function.
Mathematics
2 answers:
elena-s [515]2 years ago
8 0

Use the zeroes to determine the roots.


Write the polynomial as a product of the leading coefficient, a, and the factors, where each factor is x minus a root.


Use the y-intercept (0, –5) to solve for the leading coefficient.


Substitute the leading coefficient into the polynomial function for a and simplify.

olga_2 [115]2 years ago
7 0
1. "the graph has the same zeros" : so let a be the "triple" root of the cubic polynomial function.

2. So f(x)=(x-a)^{3}

3. Don't forget that the expression might have a coefficient b as well, and still maintain the conditions: 
 
f(x)=b(x-a)^{3}

4. Now, f(0)=-5 so  -5=f(0)=b(0-a)^{3}=b(-a) ^{3}=-ba ^{3}

-5=-ba ^{3}

5=ba ^{3}

b= \frac{5}{ a^{3} }

5. the function is f(x)=\frac{5}{ a^{3} }(x-a)^{3} where a can be any real number except 0
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