Question

which represents a quadratic function? f(x) = 2x³ + 2x² - 4 f(x) = -7x² - x + 2 f(x) = -3x + 2 f(x) = 0x² + 3x - 3

Explanation:

Step1: Recall the definition of a quadratic function

A quadratic function is a polynomial function of the form \( f(x) = ax^{2}+bx + c \), where \( a
eq0 \), and \( a \), \( b \), \( c \) are real numbers.

Step2: Analyze each option

• For \( f(x)=2x^{3}+2x^{2}-4 \): The highest power of \( x \) is 3, so it is a cubic function, not quadratic.
• For \( f(x)=-7x^{2}-x + 2 \): Here, \( a=-7

eq0 \), \( b=-1 \), \( c = 2 \), which is in the form \( ax^{2}+bx + c \) with \( a
eq0 \), so it is a quadratic function.

• For \( f(x)=-3x + 2 \): The highest power of \( x \) is 1, so it is a linear function, not quadratic.
• For \( f(x)=0x^{2}+3x - 3 \): Since \( a = 0 \), this simplifies to \( f(x)=3x - 3 \), which is a linear function, not quadratic.

Answer:

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