Identify Coefficients in the Equation 6=6x+2x²: Term Analysis

To solve this problem, we'll start by rearranging the given equation:

• Step 1: Identify the standard quadratic form: $y = ax^2 + bx + c$.
• Step 2: Rearrange $6 = 6x + 2x^2$ to fit $ax^2 + bx + c = 0$.
• Step 3: Identify coefficients $a$, $b$, and $c$.

Now, let's work through each step:
Step 1: The general form we aim for is $y = ax^2 + bx + c$.
Step 2: Rearrange the given equation:
Start by rearranging the terms to resemble $ax^2 + bx + c = 0$. We write the equation as:
$2x^2 + 6x - 6 = 0$

Step 3: Now, comparing this with the standard form $ax^2 + bx + c = 0$, we identify the coefficients:
$a = 2$
$b = 6$
$c = -6$

Therefore, the correct parameters for the equation $6 = 6x + 2x^2$ are $a = 2$, $b = 6$, and $c = -6$.

Checking against the answer choices, choice 3: $(a=2, b=6, c=-6)$ matches our result.