Find Coefficients in y=3+3x²-4x: Term-by-Term Analysis

Let's solve the problem step-by-step:

Our task is to identify the coefficients $a$, $b$, and $c$ in the quadratic function, which is written in the form $y = ax^2 + bx + c$.

The given equation is $y = 3 + 3x^2 - 4x$.

• Step 1: Rewrite the equation in the standard quadratic form $ax^2 + bx + c$. It becomes $y = 3x^2 - 4x + 3$.
• Step 2: Compare term by term with $ax^2 + bx + c$:

Upon comparison, we find:

• The coefficient of $x^2$ is $a = 3$.
• The coefficient of $x$ is $b = -4$.
• The constant term is $c = 3$.

Therefore, the parameters are:

$a = 3, b = -4, c = 3$.

The correct answer among the choices is choice 2: $a=3,b=-4,c=3$.