Find Coefficients in y=-x-3x²: Complete Polynomial Analysis

To solve this problem, we will write the given function in standard form:

The function provided is $y = -x - 3x^2$. Our goal is to express it in the standard form $y = ax^2 + bx + c$.

• Step 1: Reorder the terms: Write the quadratic term first, followed by the linear term and then the constant.

Thus, the given function becomes $y = -3x^2 - x + 0$.

• Step 2: Identify the coefficients $a$, $b$, and $c$:

From the expression $y = -3x^2 - x + 0$, we observe:

• The coefficient $a$ is -3 (from the term $-3x^2$).

• The coefficient $b$ is -1 (from the term $-x$).

• The coefficient $c$ is 0 (as there is no constant term).

Therefore, the correct choice displaying these coefficients is $a = -3$, $b = -1$, and $c = 0$, which corresponds to choice 4.

Thus, the solution is:

$a = -3, b = -1, c = 0$