Question

Write an equation for a polynomial with all the following features: The Degree is 5. The graph of the Polynomial crosses the vertical axis at y = 12. The Polynomial has 4 terms.

Answer 1

Answer: f(x) = a*x^5 + b*x^3 + c*x^2 + 12.

Step-by-step explanation:

The degree is 5, so we will have a term like:

a*x^5

it crosses the vertical axis at y = 12, then we will have a constant term equal to 12.

The polynomial has 4 terms, and we already defined two, so we can invent two more, such that the exponent must be between 1 and 4

This polynomial can be something like:

f(x) = a*x^5 + b*x^3 + c*x^2 + 12.

where a, b and c are real numbers.

Has 4 terms, f(0) = 12, then it intersects the y-axis at y = 12, and the maximum exponent is 5, then the degree of f(x) is 5.

Answer 2

The required equation of the polynomial will be expressed as $P(x) = ax^5+bx^4+cx^3+12$

The standard form of a polynomial equation with a leading degree is 5 is expressed as $P(x) = ax^5+bx^4+cx^3+dx + e$

Since the polynomial should have only 4 terms, the standard form of the equation will be $P(x) = ax^5+bx^4+cx^3+d$

d is the constant

Since the graph of the Polynomial crosses the vertical axis at y = 12, hence the constant value "d" will be 12.

Substituting the constant value, the required equation of the polynomial will be expressed as $P(x) = ax^5+bx^4+cx^3+12$

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