Question

Explain the number of solutions x^2−8x+21 and 〖(x−4)〗^2+5 have when graphed together. How do you know?

Answer 1

Graph both functions on the same set of axes (x- and y-). Then identify the coordinates of any point or points at which the two graphs intersect.

Optional: If such a point is (a,b), then the solution corresponding to that intersection is x=a, y=b.

Answer 2

Looks as tho' both functions are quadratics. Two quadratics graphed on the same set of axes could intersect at 0, 1 or 2 points.