Exercises 123–125 will help you prepare for the material covered in the next section. Solve for y: x = y² -1, y ≥ 0.

Key Concepts

Quadratic Equations

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0. In the context of the given question, the equation x = y² - 1 can be rearranged to form a standard quadratic equation in terms of y, allowing for the application of methods such as factoring or the quadratic formula to find the values of y.

Square Roots

Square roots are the values that, when multiplied by themselves, yield the original number. In solving the equation x = y² - 1, isolating y² leads to y = √(x + 1). Understanding how to manipulate square roots is essential, especially since the problem specifies y ≥ 0, indicating that only the non-negative root is relevant.

Domain and Range

The domain refers to the set of all possible input values (x-values) for a function, while the range refers to the set of possible output values (y-values). In this problem, the condition y ≥ 0 restricts the range of the solution, which is crucial for determining valid solutions to the equation and understanding the behavior of the function represented by the equation.