Find the Constant Term c in y = 3x² + 5: Quadratic Equation Analysis

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

• Step 1: Compare the given equation $y = 5 + 3x^2$ to the standard form $ax^2 + bx + c$.
• Step 2: Identify the terms corresponding to $a$, $b$, and $c$.

Now, let's work through each step:
Step 1: The given equation is $y = 5 + 3x^2$. Rearranging it in the standard form, we have $y = 3x^2 + 0\cdot x + 5$.

Step 2: From this arrangement, it's clear that:
- $a = 3$ (the coefficient of $x^2$)
- $b = 0$ (there is no $x$ term, so its coefficient is 0)
- $c = 5$ (the constant term)

Therefore, the value of $c$ is $\ c=5$.