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

To solve this problem, we will match the given quadratic equation with its standard form:

• Step 1: Identify the standard quadratic form as $y = ax^2 + bx + c$.
• Step 2: Compare with given equation $y = 4 + 3x^2 - x$.
• Step 3: Determine the coefficients by arranging the equation in standard form.

Let's now perform the steps:

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

Step 2: The given equation is $y = 4 + 3x^2 - x$.

Step 3: Rearrange the given equation to match the standard form:

$y = 3x^2 - x + 4$.

Now, directly compare:

$a = 3$

$b = -1$

$c = 4$

Therefore, the coefficients are correctly identified as $a=3, b=-1,$ and $c=4$.

The correct answer is: $a=3, b=-1, c=4$.