leikleikm18
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Suppose the graph of a cubic polynomial function has the same zeroes and passes through the coordinate (0, –5). Describe the steps for writing the equation of this cubic polynomial function.

Respuesta :

1. "the graph has the same zeros" : so let a be the "triple" root of the cubic polynomial function.

2. So f(x)=[tex] (x-a)^{3} [/tex]

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

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

[tex]-5=-ba ^{3}[/tex]

[tex]5=ba ^{3}[/tex]

[tex]b= \frac{5}{ a^{3} } [/tex]

5. the function is [tex]f(x)=\frac{5}{ a^{3} }(x-a)^{3}[/tex] where a can be any real number except 0
gubaby7

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.

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