What is the rule for this function?

What is the rule for this function?
Input: -2, Output: -4
Input: 0, Output: -2
Input: 5, Output: -3

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1 Answer

The points are not colinear so go for a quadratic: y=ax^2+bx+c. When x=0 y=-2 so c=-2 and y=ax^2+bx-2.

Plug in the points (-2,-4) and (5,-3):

-4=4a-2b-2, -2=4a-2b, -1=2a-b, b=2a+1;

-3=25a+5b-2, -1=25a+5b=25a+10a+5 substituting for b, -6=35a, a=-6/35, b=-12/35+1=23/35.

So, y=-6x^2/35+23x/35-2 is the quadratic passing through the given points.

The equation is graphically represented below:

by Top Rated User (1.2m points)

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