How do I find the "Turning Point" in a graph?

Question

I'm having trouble finding the Turning Point in a graph.

y=x^2 + 11x + 18

How do I do this?

I've found the Y intercept, the X intercepts, but I don't know how to find the Turning Point. Whoever answers the best and the fastest gets the BEST ANSWER!

Answer 1

Derive the original function

y = x^2 + 11x + 18

y' = 2x + 11

Let y' = 0

0 = 2x + 11

-11 = 2x

x = -5.5

sub -5.5 into the original function

y = -5.5^2 + 11(-5.5) + 18

y = 30.25 - 60.5 + 18

y = -12.25

TP at (-5.5, -12.25)

Graph if on your graphics calc and check it then.