Question

which represents a quadratic function?
○ $f(x) = 2x^3 + 2x^2 - 4$
○ $f(x) = -7x^2 - x + 2$
○ $f(x) = -3x + 2$
○ $f(x) = 0x^2 + 3x - 3$

Explanation:

Step1: Recall quadratic function definition

A quadratic function is a polynomial function of degree 2, with the general form \( f(x) = ax^2 + bx + c \), where \( a
eq 0 \), \( a \), \( b \), \( c \) are real numbers.

Step2: Analyze each option

• Option 1: \( f(x) = 2x^3 + 2x^2 - 4 \). The highest power of \( x \) is 3, so it's a cubic function (degree 3), not quadratic.
• Option 2: \( f(x) = -7x^2 - x + 2 \). Here, \( a = -7

eq 0 \), \( b = -1 \), \( c = 2 \), and it's in the form \( ax^2 + bx + c \) with degree 2. This fits the quadratic function definition.

• Option 3: \( f(x) = -3x + 2 \). The highest power of \( x \) is 1, so it's a linear function (degree 1), not quadratic.
• Option 4: \( f(x) = 0x^2 + 3x - 3 \). Simplifying, \( f(x) = 3x - 3 \) (since \( 0x^2 = 0 \)). The highest power of \( x \) is 1, and \( a = 0 \), so it's a linear function, not quadratic.

Answer:

\( f(x) = -7x^2 - x + 2 \) (the second option)