Need help with this maths equation!

Question

The coordinate pairs below represent points on the graph of a quadratic function. None of the points are completely identical.

(-p-1, (h²+28h)/3); (-2,(-h+p-1)/2); (3,-(p²)/4); (-11,1-11p); (-5,7); (2,0); (7,1-11p); (-6,p-6)

a. Find the values of h and p

b. Does the function have a maximum value or a minimum value? What is that value? Thoroughly explain your reasoning.

Answer 1

The way I would tackle this is to set up linear equations to solve for a, b, c, and p. That will be sufficient to determine the quadratic function. Then you can solve for h.

The points (-5,7) and (2,0) give:

4a + 2b + c = 0

25a -5b + c = 7

If we use the point: (7, 1 - 11p), we get:

49a + 7b + c +11p = 1

And if we use (-6, p - 6):

36a -6b + c - p = -6

That is four equations and four unknowns. Perhaps a Gaussian elimination calculator, or reduced row echelon form on your graphing calculator to avoid the manual effort in solving that system?

Doing so gave me: a = -1, b = -4, c =12, p = 6.

I used f(x) = -x² -4x +12 to solve for h.

Not sure this is the only way to go.