Determine whether the following quadratic function has a max

Determine whether the following quadratic function has a maximum or a minimum value. Then find the maximum or minimum value and where it occurs. f(x) = x^2+ 10x+15 Select the correct choice below and fill in the answer boxes to complete your choice (Simplify your answers) The function has a maximum value of at x=. The function has a minimum value of at x= .

Solution

f(x) = x^2 +10x +15

in quadratic equation ax^2 +bx +c if a>0 then quadratic function is upward opening.So, it would have a minima

Now minima of quadratice fuction lies at vertex (h, k)

where h = -b/2a

In our case a=1 So, f(x) has minima

At x = -b/2a = -(10/2*1) = -5

y = (-5)^2 + 10(-5) +15 = 25 -50 +15 = -35

So, minima value of -35 exists at x= -5