find the maximum y value on the graph of y=f(x)

Question

f(x)= x^2+2x+10=

Answer 1

Maximum value is infinity, since for very large x this function grows to infinity.

Answer 2

Since the coefficient of the x² term is positive, this is the graph of a parabola opening upward toward +infinity.

 

Vertex

x = -b/(2a) = -2/(2)(1) = -2/2 = -1

y = f(-b/(2a)) = f(-1) = 9.

 

Vertex

(-1, 9)

 

 

Minimum value would be 9.