Domain Analysis: Find Valid Inputs for x² + 2(17/20)

Find the positive and negative domains of the function:

$y=x^2+2\frac{17}{20}$

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

• Step 1: Understand the nature of the quadratic function
• Step 2: Determine when $y = x^2 + \frac{57}{20}$ is negative
• Step 3: Determine when it is positive

Now, let's work through each step:
Step 1: The function $y = x^2 + \frac{57}{20}$ is a parabola that opens upwards because $x^2$ is always non-negative.
Step 2: Since $x^2$ is always non-negative and $\frac{57}{20}$ is positive, $y = x^2 + \frac{57}{20}$ is always positive or zero.
Step 3: The function cannot be negative given that both terms $x^2$ and $\frac{57}{20}$ are both non-negative and positive, respectively.

However, for determining strictly positive values, it holds true for function value when $y > 0$. This occurs when $x \neq 0$, but since $y$ is indeed non negative for all reals, looking for positive domains here matters less for positive values.

Therefore, the solution to the problem is:

$x < 0 :$ none

$x > 0 :$ all x