Which of the following is the best approximation for the quadratic function containing the points (-2, 1), (-5, 2), (7, 9), and (10, 14)?
A. y=0.08x2+0.4x+1.8
B. y=1.08x2+0.4x+1.8
C. y=1.08x2−0.4x+1.8
D. y=0.08x2−0.4x+1.8

Question

Which of the following is the best approximation for the quadratic function containing the points (-2, 1), (-5, 2), (7, 9), and (10, 14)?
	A.	y=0.08x2+0.4x+1.8
	B.	y=1.08x2+0.4x+1.8
	C.	y=1.08x2−0.4x+1.8
	D.	y=0.08x2−0.4x+1.8

mathmale · Answer

Have you done this type of problem before?  If so, what do you remember of your method of attack from last time?

The standard quadratic equation has the form y=f(x) = ax^2  bx + c.  Note that there are three unknowns, namely, the parameters or coefficients a, b and c.

You are given four points that must lie on the graph of this quadratic.  Since you need to find only three unknowns / parameters / coefficients, a, b and c, you may choose any 3 of the given points at random and substitute their x-and y-coordinates into the quadratic equation. 

Doing this, you'll end up with three equation sin three unknowns.  This is sufficient info to enable you to find the values of a, b and c.

Please get started.  How would you find a, b and c?