The Maximum Value Of The Function F (X)= X^2+5x+6

The maximum value of the function f (x)= x^2+5x+6

 

Answer:

The minimum value is -1/4.

The graph or parabola opens upward because a > 0 or a is positive, therefore it has a minimum value.

Step-by-step explanation:

f(x) = x² + 5x + 6

Where:

a = 1   and b = 5

If a > 0, the parabola or graph of the equation opens upward, therefore, the given function has minimum value, NOT maximum.

The maximum or minimum value is determined by k  of the vertex (h,k) of the quadratic function.

Find the vertex (h, k) of the quadratic equation:

h = -b/2a

h = -(5)/2(1)

h = -5/2

Solve for k by substituting the value of (-5/2) to x in the given function:

f(x) = x² + 5x + 6

f(-5/2) = (-5/2)² + 5(-5/2) + 6

k = (25/4) - 25/2 + 6

LCD: 4

k = 25/4 - 50/4 + 24/4

k = -25/4 + 24/4

k = - 1/4

The minimum value is -1/4.

Vertex: (-5/2, -1/4)