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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.

 Jun 10, 2022
 #1
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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

 

 

 

 

 

cool cool cool

 Jun 10, 2022

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