MATHEMATICS · Multi-part · AoPS · Mathematics · Special Functions · Special Functions
Problem
Let p(x)=x2−4x+3 and q(x)=∣x−1∣.
(i) On the same coordinate plane, sketch the graphs of y=p(x) and y=q(x), showing all intercepts and the vertex of the parabola.
(ii) Using your sketches (or otherwise), determine the number of real solutions of the equation p(x)=q(x) and state approximate values of the solutions correct to one decimal place.
(iii) Find the least real value of x that satisfies p(x)=q(x).