Let's explore the given polynomial equation [tex]\( y = 2x^2 + x + 2 \)[/tex] step-by-step:
1. Equation Analysis:
We start with the quadratic equation in [tex]\( x \)[/tex]:
[tex]\[
y = 2x^2 + x + 2
\][/tex]
2. Identify the Coefficients:
The quadratic equation is in the standard form [tex]\( y = ax^2 + bx + c \)[/tex], where:
- [tex]\( a = 2 \)[/tex] (coefficient of [tex]\( x^2 \)[/tex])
- [tex]\( b = 1 \)[/tex] (coefficient of [tex]\( x \)[/tex])
- [tex]\( c = 2 \)[/tex] (constant term)
3. Purpose:
Since we aren't given a specific [tex]\( y \)[/tex] value (e.g., to find roots or a specific point), we generally analyze the polynomial itself.
4. Polynomial Expression:
The polynomial [tex]\( y = 2x^2 + x + 2 \)[/tex] is simply represented in its expanded form. This expression shows how [tex]\( y \)[/tex] changes based on the value of [tex]\( x \)[/tex].
The detailed expression of the polynomial remains:
[tex]\[
y = 2x^2 + x + 2
\][/tex]
5. Conclusion:
Given the polynomial [tex]\( y = 2x^2 + x + 2 \)[/tex], the form already represents the detailed result of the equation. There are no further steps required for calculations or transformations unless additional information or constraints are provided.
Thus, the expression [tex]\( y = 2x^2 + x + 2 \)[/tex] fully and correctly describes the polynomial equation as given.
