Answer to Question #250538 in Calculus for bri

Question

b. Discuss the possibilities for the number of times the graphs of two different quadratic functions intersect?

Answer 1

A parabola is a curve that defined by the general equation which is written as:

$f(x)= ax^{2}+bx+c$

$g(x)= px^{2}+qx+r$

For solving to find point of intersection, let equalize two equations:

$ax^{2}+bx+c = px^{2}+qx+r$

$(a-p)x^{2}+(b-q)x+(c-r) = 0$

The above equation can have 1, 2 or zero solutions. Based on this, it can say that the graphs of two different quadratic functions may intersect at one or two points or may not intersect.