Question

which function is a quadratic function?

\\(c(x) = 6x + 3x^3\\)
\\(d(x) = x - 8x^4\\)
\\(p(x) = -5x - x^2\\)
\\(k(x) = 2x^2 + 9x^4\\)

Explanation:

Identify the definition of a quadratic function

A quadratic function is a polynomial function of degree 2, which can be written in the standard form \(f(x) = ax^2 + bx + c\), where \(a
eq 0\).

Analyze the degree of each given function

• \(c(x) = 6x + 3x^3\): The highest exponent of \(x\) is 3 (cubic function).
• \(d(x) = x - 8x^4\): The highest exponent of \(x\) is 4 (quartic function).
• \(p(x) = -5x - x^2\): The highest exponent of \(x\) is 2 (quadratic function).
• \(k(x) = 2x^2 + 9x^4\): The highest exponent of \(x\) is 4 (quartic function).

Determine the correct option

The only function with a degree of exactly 2 is \(p(x) = -5x - x^2\).

Answer:

• (A) \(c(x) = 6x + 3x^3\)
• (B) \(d(x) = x - 8x^4\)
• (C) \(p(x) = -5x - x^2\) (Correct answer)
• (D) \(k(x) = 2x^2 + 9x^4\)