Final answer:
We set quadratic equations to zero because it is necessary for finding the solutions or roots using the quadratic formula and simplifies other solving methods.
Step-by-step explanation:
We set quadratic equations equal to zero because it's required to find the solutions or roots using the quadratic formula. The standard form of a quadratic equation is ax² + bx + c = 0. By setting the quadratic equation to zero, we directly apply the quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a), to solve for the variable x. This method allows us to find the points where the quadratic function intersects the x-axis, which correspond to the x-values when the y-value is zero.
Ensuring the equation is in the form ax² + bx + c = 0 also simplifies the process of solving it by other methods, like factoring or completing the square. It can further reveal information about the graph of the quadratic function, like its vertex and axis of symmetry.