Parabolas y=−2x^2 and y=2x^2 +k intersect at points a and b that are in the third and the fourth quadrants respectively. find k if length of the segment ab is 5.

-25  

Step-by-step explanation:

(1)   y = -2x²

(2) y =   2x² + k     Subtract (1) from (2)

    0 =  4x² + k      Subtract 4x² from each side

    k = -4x²

The parabolas are symmetrical about the y-axis.

Segment AB = 5, so x = +2.5 and x = +2.5.

k = -4(±2.5)² = -4 × 6.25 = -25