Okay, here we have this:
Considering the provided function, we are going to convert it to vertex form and to find the minimum value of f(x), so we obtain the following:
Vertex form:
f (x) = x^2 + 14x + 36
y - 36 = x^2 + 14x
y - 36 + (14/2)^2 = x^2 + 14x + (14/2)^2
y - 36 + 49 = x^2 + 14x + 49
y +13 = (x+7)^2
f(x)= (x+7)^2 - 13, This is the function in vertex form.
Minimum value of f (x):
To calculate the minimum then we will find the vertex:
To calculate the minimum then we will find the vertex: x=-b/(2a)
x=-b/(2a)
x=-14/(2*1)
x=-14/2
x=-7
And the y-coordinate will be:
f(-7)=(-7+7)^2 - 13
f(-7)=(0)^2 - 13
f(-7)=- 13
Finally we obtain that the minimum value of f(x) is -13.
Considering the provided function, we are going to convert it to vertex form and to find the