F(x)=1/4 (x+7)^2+7 Looking for the vertex and the max or min for the above..?
And thank you for checking my work, nice to know I get some of it.
sorry i didn't see that for some reason on your other post lol
k i would rewrite this first equation a bit so it is in vertex form
vertex form is written like this : f(x)=a(x-h)^2 + k
to rewrite it in this form it will look like this
f(x)= a(x-(-7))^2 +7
a = 1/4 k= 7 h=-7
vertex is (h, k) = (-7, 7)
min/,max is always at the vertex so f(x)=7
oh by the way since a=1/4 that means a > o meaning graph opens upward and the vertex point f(-7)=7 is a minimum point
To find the vertex and determine if it corresponds to the maximum or minimum point of the function f(x)=1/4(x+7)^2+7, we can use the concept of vertex form, which is expressed as f(x) = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex.
In our given function f(x) = 1/4(x+7)^2 + 7, we can identify that a = 1/4, h = -7, and k = 7. Thus, the vertex is at the point (-7, 7).
Now, let's determine if this vertex corresponds to a maximum or minimum point. Since the coefficient 'a' in the vertex form determines the concavity of the parabola, if 'a' is positive, the parabola opens upward, indicating a minimum point. Conversely, if 'a' is negative, the parabola opens downward, suggesting a maximum point.
In our case, a = 1/4, which is positive. Consequently, the vertex (-7, 7) corresponds to the minimum point of the function f(x).
Hence, the vertex is (-7, 7), and it represents the minimum point of the function.