Question 340916: Use complete sentences to explain how you would use graphing technology to find the solutions of 0 = −x^2 + 2.5x + 1. What do the solutions of 0 = −x2 + 2.5^x + 1 represent on the graph of the equation? Answer by solver91311(16897) (Show Source):
René Descartes started with "I think, therefore I am." While quite short, that is a complete sentence.
The values of that make the equation a true statement are the -coordinates of the points where the graph of the analogous quadratic function intersect the -axis, if any exist. In this case, since the signs on the lead coefficient and the constant term are opposite, you are guaranteed that the graph of the function will intersect the -axis in two distinct points, and therefore the equation will have two distinct real roots.
My calculator said it, I believe it, that settles it