Find Coefficients in y=-x² + 3x + 40: Quadratic Equation Analysis

To solve this problem, we will follow these steps:

• Step 1: Identify the given quadratic equation and its form.
• Step 2: Directly match the coefficients of the given equation to the standard form $y = ax^2 + bx + c$.
• Step 3: Compare with the provided choices and select the one that matches.

Now, let's work through each step:
Step 1: The given quadratic equation is $y = -x^2 + 3x + 40$. This matches the form $y = ax^2 + bx + c$.

Step 2: By comparing the given equation to the standard form:
- The coefficient $a$ is the coefficient of $x^2$, which is $-1$.
- The coefficient $b$ is the coefficient of $x$, which is $3$.
- The coefficient $c$ is the constant term, which is $40$.

Step 3: From the analysis, we identify $a = -1$, $b = 3$, $c = 40$. We compare these with the provided choices.
The correct answer is: $a=-1,b=3,c=40$

Therefore, the solution to the problem matches choice 4.