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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.

 May 1, 2022
 #1
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Note that if  we have the parabola

 

y= (1/2)(x -1)(x + 2)

The roots  are 1  and -2  and the y intercept = -1

So.....the area of this  triangle  =  (1 - - 2) /  (  2 * 1 )  =  1.5

If we let k  = 2

Then   (k + 1) ( 1*k)  =   (2 + 1)  (1(2))  / 2 =   twice the area of this triangle 

 

Also  if we let k =  -2   then  ( -2  - 1) ( 1*-2))/ 2  =  twice the area 

 

y = (1/2)(x - 3.5)(x + k)

 

This implies  that

 

(k + 3.5) (3.5k) / 2  =  3

k ≈ .436

k≈ -3.93559  

 

Also

( k - 3.5) (3.5k)/2 = 3

k ≈  - .435

k ≈ 3.93559

 

 

cool cool cool

 May 1, 2022

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