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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.

 Aug 3, 2021
 #1
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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:

 

 Aug 4, 2021

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