You are studying the graph of the quadratic function where
MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions
Problem
You are studying the graph of the quadratic function y=ax2+bx+c where a=0. Answer the following questions to show how algebraic information about the quadratic relates to its graph.
(i) Define the discriminant of a quadratic equation in one variable.
(ii) State how the sign of the discriminant determines the number of real roots of the equation ax2+bx+c=0.
(iii) Using rough sketches of parabolas, illustrate the three possible cases you have listed in part (ii). In each sketch clearly show the x–axis, the points of intersection (if any), and the direction in which the parabola opens.