Find Coefficients in y = 3x² - 81: Quadratic Equation Analysis

To solve this problem, we will identify values of $a$, $b$, and $c$ in the quadratic function:

• Step 1: Note the given equation $y = 3x^2 - 81$.
• Step 2: Compare it to the standard quadratic form $y = ax^2 + bx + c$.
• Step 3: Match coefficients to find $a$, $b$, and $c$.

Now, let's work through each step:
Step 1: The given equation is $y = 3x^2 - 81$.
Step 2: Compare this to the standard form, $y = ax^2 + bx + c$. In this equation:
- The coefficient of $x^2$ is 3, hence $a = 3$.
- There is no $x$ term, which means $b = 0$.
- The constant term is $-81$, hence $c = -81$.

Therefore, the solution to the problem is $a = 3, b = 0, c = -81$.