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.
+128475 If y = 0.......then the x intercepts are 3.5 and -k
If x = 0 the y intercept = .5 (- 3.5) (k) = -1.75k
So any triangle formed will have the area of 1.5 expressed as
(1/2) ( 3.5 - k) (-1.75k) = 1.5 multiply through by 2
(3.5 - k) (-1.75 k) = 3 simplify
(7/2 - k) ( -7/4k) = 3
(7/4)k^2 - (49/8)k - 3 = 0 multiply through by 8
14k^2 - 49k - 24 = 0
Using the Quadratic formula
49 ± √ [ 49^2 - 4 (14)(-24) ]
k = ________________________ ≈ 3.96 or ≈ -.436
2 * 14
