Th graph of a quadratic function f(x)=hx²-12x+3k, where h and k are constants, has a minimum point.
(a)state the value of h, if -2＜h＜2 where h is an integer
(b)based on the answer in (a),find the value of k if the graph touches x-axis at one point

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)

sas (side angle side)

aa (angle angle)

sss(side side side)

sas find two sides with an angle in between

aa is finding two angles and the third will add up to 180

sss find all sides

step-by-step explanation:

divide the numbers

step-by-step explanation: