Question

Find a parabola with equation y=ax^2+bx+c that has a slope 10 at x=1, slope -26 at x=-1, and passes through the point (2,29)

Answer 1

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Answer:

y = 9x^2 -8x +9

Explanation:

The given equation has derivative ...

y' = 2ax +b

The requirements on slope give rise to two equations:

2a(1) +b = 10

2a(-1) +b = -26

Adding these equations together gives ...

2b = -16 ⇒ b = -8

Then we have ...

2a -8 = 10

a = (10 +8)/2 = 9

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The given point lets us find the constant term c.

y = 9x^2 -8x +c

c = y -(9x -8)x = 29 -(9(2) -8)(2) = 29 -20 = 9

The equation of the parabola is ...

y = 9x^2 -8x +9