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Marta_Voda [28]
3 years ago
14

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.

Mathematics
1 answer:
OverLord2011 [107]3 years ago
8 0

Answer:

-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 <em>symmetrical about the y-axis.</em>

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

k = -4(±2.5)² = -4 × 6.25 = -25

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