state the equation of the graph above

Question

Point:

(0,3)

(1,0)

(2,-1)

(3,0)

Answer 1

Since there are 2 x-intercepts, a first guess might be a quadratic function of the form y = a(x-1)(x-3), which contains the points (1,0) and (3,0).

 

Since (2, -1) has to be on the curve, -1 = a(1)(-1).  So, a = 1.

 

This gives y = (x-1)(x-3).  Plugging in the point (0,3), we see that (0,3) also lies on the curve.

 

A function which passes through the given points is f(x) = x² - 4x + 3.