Find the Coefficients in y=5x-3x²: Polynomial Term Analysis

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

• Step 1: Express the given quadratic function $y = 5x - 3x^2$ in the standard form.
• Step 2: Compare the given function with the standard form $y = ax^2 + bx + c$.
• Step 3: Match the coefficients to find the values of $a$, $b$, and $c$.

Now, let's work through each step:

Step 1: The given function is $y = 5x - 3x^2$.

Step 2: We need the function in the form $y = ax^2 + bx + c$. Reordering terms gives us $y = -3x^2 + 5x$.

Step 3: Comparing $y = -3x^2 + 5x$ to $y = ax^2 + bx + c$, we identify:

• The coefficient of $x^2$ is $a = -3$.
• The coefficient of $x$ is $b = 5$.
• The constant term (often written last) is $c = 0$ since no constant term is present.

Therefore, the solution to this problem is the coefficients identified as $a = -3$, $b = 5$, and $c = 0$.