Create an Algebraic Expression Using a = 1/2, b = 1/2, c = 1/2

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

• Step 1: Identify and substitute the values of $a$, $b$, and $c$ into the equation $y = ax^2 + bx + c$.
• Step 2: Simplify the equation to obtain the required expression.
• Step 3: Compare the simplified expression with the provided multiple-choice answers.

Let's work through each step:

Step 1: The given coefficients are $a = \frac{1}{2}$, $b = \frac{1}{2}$, and $c = \frac{1}{2}$. Substitute these values into the standard quadratic form $y = ax^2 + bx + c$:

$y = \frac{1}{2}x^2 + \frac{1}{2}x + \frac{1}{2}$

Step 2: The expression is already simplified. The coefficients are correctly substituted, and no further simplification is needed:

$y = \frac{x^2}{2} + \frac{x}{2} + \frac{1}{2}$

Step 3: Compare this expression to the provided multiple-choice options. The correct match is:

Choice 1: $\frac{x^2}{2} + \frac{x}{2} + \frac{1}{2}$

Therefore, the algebraic expression is $\frac{x^2}{2} + \frac{x}{2} + \frac{1}{2}$.