Oh boy I can do this problem! =D
y = x2 + 8x - 9
We need to take the derivative of this. That will tell us the slope of the graph of this function at any point. Take the derivative using the power rule.
y' = 2x + 8
Set y' = 0 to find all the places where the slope of x2 + 8x - 9 is zero.
0 = 2x + 8
-8 = 2x
-4 = x
So when x is -4, the slope of x2 + 8x - 9 is zero. That means it is either a maximum, minimum, or inflection point. To figure out which one, take the second derivative.
Since y'' is positive when x is -4, that means the graph is concave up, which means x = -4 is the minimum.