The area of the triangle formed by x- and y-intercepts of the parabola y=5(x-3)(x+k) is equal to 1.5 square units. Find all possible values of k.

Guest Aug 3, 2021

#1**+2 **

x =3 is one of the zeroes....this would be one of the legs of the triangle....the other would occur on the y axis and needs to be = |1| for the area (1/2 b*h) = 1.5

the y axis crossing occurs when x = 0

-1 = 5 (x-3)(x+k) sub in x = 0

-1/5 = (-3)(k)

k = 1/15

when y = +1 1 = 5 (0-3((0+k )

1/5 = - 3k

k = - 1/15

Here is a desmos graph:

ElectricPavlov Aug 4, 2021