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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.

 Jul 31, 2021
 #1
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y = 0.5(x-3.5)(x+k) 

 

        when x = 0       1.75k  = y intercept

        when y = 0         x = 3.5  or -k  = x intercept  

 

Formula for area of a triangle 1/2 b h      or     1/2  x intercept * y intercept    for this problem

1/2  (1.75k  *  3.5) = 1.5

     k = .4897959

 

1/2 ( 1.75k * (-k)) = 1.5

    k = imaginary

 

I often verify answers like these with Desmos.....here is a picture:

 

 Jul 31, 2021

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