Answer:
K = -1 or -2
Explanation:
Given the equation of parabola is, y = 0.5(x-3)(x+k).
Finding y-intercept, put x=0 and solve for y :-
y = 0.5(0-3)(0+k)
y = 0.5(-3)(k)
y = -1.5k
Finding x-intercepts, put y=0 and solve for x :-
0 = 0.5(x-3)(x+k)
(x-3)(x+k) = 0
x = 3 OR x = -k
So, the coordinates of triangle ABC are:-
A(0, -1.5k), B(3, 0), and C(-k, 0)
Assuming origin O(0,0), find the area of triangle ABC:-
Area = (1/2) * BC * OA
Area = (1/2) * (k+3) * (1.5k)
But given the area is 1.5 square units.
So, (1/2) * (-k-3) * (1.5k) = 1.5
(1/2) * (-k-3) * (k) = 1
k(-k-3) = 2
-k² -3k -2 = 0
k² +3k +2 = 0
k² +2k +k +2 = 0
(k+2)(k+1) = 0
So, k = -1 or k = -2