Find Coefficients in the Equation y=4+3x-x²: Term-by-Term Analysis

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

• Step 1: Identify the standard form of a quadratic function $y = ax^2 + bx + c$.
• Step 2: Rearrange the given function $y = 4 + 3x - x^2$ to match the standard form.
• Step 3: Compare the terms and determine the values of $a$, $b$, and $c$.

Now, let's work through these steps:

Step 1: The standard form of a quadratic equation is $y = ax^2 + bx + c$.

Step 2: The provided function is written as $y = 4 + 3x - x^2$. We can rearrange this in descending order of $x$ to become $y = -x^2 + 3x + 4$, which aligns more closely with the standard form.

Step 3: By comparing the rearranged equation $y = -x^2 + 3x + 4$ with the standard form $y = ax^2 + bx + c$, we can determine:

• The coefficient of $x^2$ is $-1$, hence $a = -1$.
• The coefficient of $x$ is $3$, thus $b = 3$.
• The constant term is $4$, so $c = 4$.

Therefore, the values of $a$, $b$, and $c$ are $a = -1$, $b = 3$, and $c = 4$.