f(x)=1/4 (x+7)^2+7
f(-7)=7 min or max? How does graph open up, bottom or topside?
the graph opens to the top.
Calculus: f'= 1/2 (x+7)=0
x=-7 is location of min. Checking.
f"=1/2 positive, so at x=-7, rate of increase in f(x) is positive, so x=-7 is a min.
Thank you sir.
To determine whether the function has a minimum or maximum value, we need to examine the coefficient of the squared term in the equation.
In this case, the function f(x) = 1/4 (x + 7)^2 + 7 is in vertex form, which is represented as f(x) = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola.
In the given equation, we can see that the squared term is (x + 7)^2. When looking at the sign of the coefficient in front of the squared term, which is positive (1/4), it indicates that the parabola opens upward. This means that the graph faces upwards, resembling a "U" shape.
Regarding the vertex (h, k), in the given equation, h = -7 and k = 7. The vertex represents either the minimum or maximum point of the parabola.
To determine whether it is a minimum or maximum, we consider the sign of the coefficient 'a' in front of the squared term. Since a is positive (1/4), the parabola opens upward, and the vertex is a minimum point. Therefore, f(-7) = 7 represents the minimum value of the function.
In summary, the given function f(x) = 1/4 (x + 7)^2 + 7 has a minimum value at f(-7) = 7, and the graph opens upward, forming a 'U' shape.