Final answer:
Find the fixed points of a quadratic function by setting the equation equal to zero and applying the quadratic formula with the specific constants to calculate the solutions, which represent the x-intercepts or fixed points.
Step-by-step explanation:
To find the fixed points of a quadratic function, we must first understand that fixed points are where the function intersects the x-axis, which means they are the roots or solutions of the function when set equal to zero. Given a quadratic function in the standard form ax² + bx + c = 0, the solutions can be found by applying the quadratic formula:
√x = (-b ± √(b² - 4ac)) / (2a)
For example, if we have constants a = 1.00, b = 10.0, and c = -200, the fixed points are found by substituting these values into the quadratic formula. In equilibrium problems, analyzing square roots and real roots are essential, and frequently only the positive values are significant when dealing with quadratic equations derived from physical data. Understanding how to graph these equations in two dimensions (x-y graphing) can also provide visual representation of these fixed points.