1. What is the Y Squared Function?

The Y Squared Function represents the mathematical equation y² = x, which describes a parabola opening to the right. For each positive x value, there are two corresponding y values (positive and negative square roots).

2. How Does the Calculator Work?

The calculator solves the equation:

For any given x value ≥ 0, the calculator computes:

• \( y = \sqrt{x} \) (positive root)
• \( y = -\sqrt{x} \) (negative root)

Note: For x < 0, there are no real solutions since the square of a real number cannot be negative.

3. Mathematical Properties

Details: The function y² = x represents a parabola with its vertex at the origin (0,0), symmetric about the x-axis, and opening to the right. It's the inverse relation of the more common x = y² parabola.

4. Using the Calculator

Tips: Enter any non-negative x value. The calculator will return both positive and negative y solutions that satisfy the equation y² = x.

5. Frequently Asked Questions (FAQ)

Q1: Why are there two solutions for each x value?
A: Because both positive and negative numbers squared give the same result. For example, both 2² and (-2)² equal 4.

Q2: What happens if I enter a negative x value?
A: The equation has no real solutions for x < 0 since the square of any real number is always non-negative.

Q3: Can this function be graphed?
A: Yes, the graph is a parabola opening to the right, symmetric about the x-axis, with vertex at the origin.

Q4: What are some real-world applications?
A: This function appears in physics (projectile motion), engineering (parabolic reflectors), and economics (certain cost functions).

Q5: How is this related to the square root function?
A: The square root function y = √x gives only the principal (non-negative) root, while y² = x includes both positive and negative solutions.