State the maximum/minimum of the function h(x)=−1/2x^2+4x−5.

is noteworthy that the leading term has a negative coefficient, meaning this parabola is opening downwards like a "camel hump", so it reaches a maximum point and then goes back down, and of course the maximum point is at its vertex.

(4, -3)

Step-by-step explanation:

I'm assuming that you meant  H(x) = -(1/2)x^2 + 4x - 5.  Here, the coefficients of this quadratic are a = -1/2, b = 4 and c = -5.

The axis of symmetry is x = -b/(2a).  This axis goes through the vertex.  Here the axis of symmetry is  x = -(4) / [ 2(-1/2) ], or x = 4.

Evaluating H(x) at x = 4 gives us the y value of the vertex.  It is:

H(4) = (-1/2)(4)^2 + 4(4) - 5, or H(4) = -8 + 16 - 5, or 3.

We know that this function must have a max because a is - and therefore the graph opens down.

The vertex and the maximum is (4, 3).

if x = 1, then the answer is 3.5

the answer is 99.