Help finding equation of a parabola???

Question

I need to find the equation of the quadratic function described.

The maximum value of g is g(-1)=6 and g(-3)=4

I know that means that it goes through (-1,6) and (-3,4), but how do I find the equation?

Thank you!!!

Answer 1

2 data points do not a function make.

I could give you a function for a straight line that passes through those points, but it wouldn't be right.  A third point (maybe a y-intercept) would then give us enough information to define a function.

Answer 2

A parabola can be represented by the equation:

(Y-Y1)^2 = 4a(X - X1) . Thus for the given coordinates;

1. (Y - 6)^2 = 4a(X +1)

2. (Y - 4)^2 = 4a (X+3)

Dividing Eq.1 by Eq.2 gives:

3. (Y -6)^2/(Y - 4)^2 = (X + 1)/(X + 3)

4. ((Y - 6)^2)(X + 3) = ((Y - 4)^2)(X + 1)

Expand the expressions and bring all the terms to the left and equate it to zero to get the general equation of the parabola. Note that the given equations are for a parabola opening to the left and right of the y - axis. For parabolas opening downward and upward use:

(X - X1)^2 = 4a(Y -Y1)