why does 3x^2+ 2x +14 get smaller when i do 3(-x)^2 + 2(-x) +14?
Thanks
It doesn't. $\displaystyle g(x) = f(-x) = 3(-x)^2 + 2(-x) +14$ is the reflection of f(x) in the y-axis. There will be some values of x for which f(x) > f(-x) and some for which f(x) < f(-x), since the line of symmetry of f(x) is NOT the y-axis. But f(-x) will not be smaller than f(x) for all values of x .....
In fact:
f(x) = f(-x) for x = 0
f(x) < f(-x) for x < 0
f(x) > f(-x) for x > 0
Note also that each graph has the same minimum value of y, namely 41/3 ...... It occurs at x = -1/3 for y = f(x) and x = 1/3 for y = f(-x).