Question
1. A polynomial function of the second degree has what form?
Ask by Bartlett Clark. in Papua New Guinea
Mar 10,2025
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Tutor-Verified Answer
Answer
A second-degree polynomial function is of the form \( f(x) = ax^2 + bx + c \), where \( a \), \( b \), and \( c \) are constants, and \( a \) is not zero.
Solution
1. A polynomial function of the second degree, also known as a quadratic function, can be written in the form
\[
f(x) = ax^2 + bx + c
\]
where:
- \(a\), \(b\), and \(c\) are constants.
- \(a \neq 0\) (if \(a = 0\), the function would not be of the second degree).
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Simplify this solution Extra Insights
Polynomial functions of the second degree, also known as quadratic functions, take the form \( f(x) = ax^2 + bx + c \), where \( a \), \( b \), and \( c \) are constants, and \( a \) is not equal to zero. The graph of a quadratic function is a parabola that opens upwards if \( a > 0 \) and downwards if \( a < 0 \). Quadratic functions are not just theoretical; they model a variety of real-world situations! For example, they can describe the trajectory of a ball thrown into the air, the area of a rectangle as its dimensions change, or even the profit calculations of a business. Understanding these functions helps predict outcomes in many fields, from physics to finance!
