Answer:
h = 1
k = 12.
Step-by-step explanation:
(A).
f(x ) = hx² - 12x + 3k
Convert to vertex form ( vertex form is a(x - b)^2 + c ):-
f(x) = h (x^2 - 12x/h) + 3k
= h [ (x - 6/h)^2 - 36h^2 ] + 3k
= h(x - 6/h)^2 - (36/h - 3k).
So the vertex is at x = 6/h.
h must be positive because the function has a minimum value.
h < 2 so as its an integer it must be 1.
(B)
The vertex is at ( 6/h , -(36/h-3k) ).
If the graph touches the axis at one point then the vertex is (6/h , 0)
and - (36/h - 3k) = 0
-36 = -3k
k = 12 (answer)
