Final answer:
The function y = x² is a quadratic function, and in translation notation, it can be written as f(x) = (x - d)² when shifted to the right by a distance d. To solve for a variable that is squared, such as finding a side of a triangle using the Pythagorean theorem, the square root is used.
Step-by-step explanation:
The type of function represented by y = x² is a quadratic function. In translation notation, if we wanted to shift this function horizontally by a value d, we would rewrite the function as f(x) = (x - d)² for a shift to the right, or f(x) = (x + d)² for a shift to the left. To "undo" a square when solving equations like the Pythagorean theorem, we take the square root, which is the inverse function of squaring.
For example, if the hypotenuse c of a right triangle is known, and one side b is known, the other side a can be found using a = √(c² - b²). The general form of a quadratic equation is y = ax² + bx + c, and it is a second-order polynomial.