Coefficient Identification in y=-6+x²+6x: Breaking Down Terms

To solve this problem, we'll follow these steps:

• Step 1: Identify the given equation
• Step 2: Reorganize the equation to match the standard form of a quadratic equation
• Step 3: Compare the terms to determine the coefficients $a$, $b$, and $c$

Now, let's work through each step:
Step 1: The provided equation is $y = -6 + x^2 + 6x$.
Step 2: Rearrange the terms to match the standard form $y = ax^2 + bx + c$. This gives us $y = x^2 + 6x - 6$.
Step 3: Compare the terms:
The coefficient of $x^2$ (the squared term) is $a$. Hence, $a = 1$.
The coefficient of $x$ (the linear term) is $b$. Hence, $b = 6$.
The constant term is $c$. Hence, $c = -6$.

Therefore, the solution to the problem is that the coefficients are $a = 1, b = 6, c = -6$.