The area of the triangle formed by x- and y-intercepts of the parabol y=0.5(x-3.5)(x+k) is equal to 1.5 square units. Find all possible values of k.
+128631 Note that if we have the parabola
y= (1/2)(x -1)(x + 2)
The roots are 1 and -2 and the y intercept = -1
So.....the area of this triangle = (1 - - 2) / ( 2 * 1 ) = 1.5
If we let k = 2
Then (k + 1) ( 1*k) = (2 + 1) (1(2)) / 2 = twice the area of this triangle
Also if we let k = -2 then ( -2 - 1) ( 1*-2))/ 2 = twice the area
y = (1/2)(x - 3.5)(x + k)
This implies that
(k + 3.5) (3.5k) / 2 = 3
k ≈ .436
k≈ -3.93559
Also
( k - 3.5) (3.5k)/2 = 3
k ≈ - .435
k ≈ 3.93559
