Identify Coefficients in y=6x+3x²-4: Polynomial Term Analysis

To solve this problem, we'll proceed with the following steps:

• Step 1: Rewrite the given quadratic function $y = 6x + 3x^2 - 4$.
• Step 2: Compare the equation to the standard form of a quadratic equation $y = ax^2 + bx + c$.
• Step 3: Identify and assign the values of coefficients $a$, $b$, and $c$.

Now, let's execute these steps:

Step 1: The given function is already $y = 6x + 3x^2 - 4$.

Step 2: The standard form of a quadratic equation is $y = ax^2 + bx + c$.

Step 3: Upon comparison, we can observe:

• The coefficient of $x^2$ is 3, so $a = 3$.
• The coefficient of $x$ is 6, so $b = 6$.
• The constant term is $-4$, so $c = -4$.

Therefore, the solution is $a=3, b=6, c=-4$. This corresponds to choice 1.