which equation represents a quadratic function with a leading coefficient of 2 and a constant term of…

Explanation:

Step1: Recall quadratic function form

A quadratic function is of the form $f(x)=ax^{2}+bx + c$, where $a\neq0$, $a$ is the leading - coefficient, $b$ is the coefficient of the linear term, and $c$ is the constant term.

Step2: Check each option

• Option 1: $f(x)=2x^{3}-3$ is a cubic function (degree 3), not quadratic.
• Option 2: $f(x)=-3x^{2}-3x + 2$ has leading coefficient $a=-3$, not 2.
• Option 3: $f(x)=-3x^{3}+2$ is a cubic function (degree 3), not quadratic.
• Option 4: $f(x)=2x^{2}+3x - 3$ has leading coefficient $a = 2$ and constant term $c=-3$, which meets the requirements.

Answer:

$f(x)=2x^{2}+3x - 3$