Answer:
I can not see the image to see where is the box, so i will answer this in a more general way.
For a general quadratic equation:
y = f(x) = a*x^2 + b*x + c
The vertex form si:
y = a*(x - h)^2 + k
Where (h, k) is the vertex of our quadratic function.
such that h = -b/2*a
and k = f(h)
Then the first step here is to find the vertex of our quadratic function.
Our quadratic function is:
y = 8*x - 4*x^2 + 5
Let's rewrite this as:
y = f(x) = -4*x^2 + 8*x + 5
then we have:
a = -4
b = 8
c = 5
Then here we have:
h = -b/(2*a) = -8/(2*-4) = -8/-8 = 1
h = 1
now to find the value of k we use:
k = f(1) = -4*1^2 + 8*1 + 5 = 9
Then we have:
h = 1
k = 9.
Then the vertex form of our function is:
y = -4*(x - 1)^2 + 9
