Analyze the Quadratic Function: y = 2x² + 3 in Standard Form

To solve this problem, we will follow these steps:

• Step 1: Identify each term in the given function $y = 2x^2 + 3$.
• Step 2: Compare the equation to the standard quadratic form $y = ax^2 + bx + c$.
• Step 3: Determine the coefficients $a$, $b$, and $c$.
• Step 4: Match these coefficients to the correct multiple-choice option.

Step 1: The given function is $y = 2x^2 + 3$. There is no $x$ term present.

Step 2: Compare this with the standard form $y = ax^2 + bx + c$:

• The coefficient of $x^2$ is $a = 2$.
• The coefficient of $x$ is $b = 0$ because there is no $x$ term.
• The constant term is $c = 3$.

Step 3: Therefore, the coefficients are $a = 2$, $b = 0$, and $c = 3$.

Step 4: Review the multiple-choice options provided:

• Choice 1: $a = 0$, $b = 2$, $c = 3$
• Choice 2: $a = 0$, $b = 3$, $c = 2$
• Choice 3: $a = 2$, $b = 0$, $c = 3$
• Choice 4: $a = 3$, $b = 0$, $c = 2$

The correct choice is Choice 3: $a = 2$, $b = 0$, $c = 3$.

Therefore, the solution to the problem is the values $a = 2$, $b = 0$, $c = 3$ which correspond to choice 3.