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

Question

natali 33

1 month 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:

Svet_ta [12.7K] · Answer 1 · 2026-02-27T17:05:43+03:00

Identify the roots using the zeroes.

Express the polynomial as a product of the leading coefficient, a, paired with factors, each of which is x subtracting a root.

Utilize the y-intercept (0, –5) to find the value of the leading coefficient.

Insert the leading coefficient as a into the polynomial function and simplify the expression.

Zina [12.3K] · Answer 2 · 2026-02-27T17:05:04+03:00

1. "The graph has identical zeros": let a represent the "triple" root of the cubic polynomial function.

2. Therefore, f(x)= $(x-a)^{3}$

3. Remember that the expression could also include a coefficient b, maintaining the same criteria:

$f(x)=b(x-a)^{3}$

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

$-5=-ba ^{3}$

$5=ba ^{3}$

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

5. The function is $f(x)=\frac{5}{ a^{3} }(x-a)^{3}$ where a may be any non-zero real number.