Question 155098: find a quadratic equation where f(2)=16 and the minimum value of f is f(-2)=-16
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! find a quadratic equation where f(2)=16 and the minimum value of f is f(-2)=-16
----------------------------------
Plot those points and you will see that f(-6) = 16 by symmetry about
the x-axis
-----------------
So you have three points: (-6,16),(-2,-16),(2,16)
----------------------------------------------------
Substitute these into ax^2 + bx + c = y
to get three equations with unknowns a,b, and c.
36a -6b + c = 16
4a -2b + c =-16
4a +2b + c = 16
-------------------------
Use any method to solve this system to get:
a = 2
b = 8
c =-8
---------------
EQUATION:
y = 2x^2 + 8x -8
==========================
Cheers,
Stan H.
|
|
|
