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Tanya [424]
2 years ago
11

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)

Mathematics
1 answer:
Hatshy [7]2 years ago
6 0

9514 1404 393

Answer:

  y = 9x^2 -8x +9

Step-by-step 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

__

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

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Determine the equation of the line that is parallel to the given line, through the given point
bixtya [17]

The equation of the line that is parallel to the given line, through the given point is y = -5x - 7

Given equation,

y = -5x + 1

Slope = m

          = -5

For two lines to be parallel, slope is equal.

Therefore, m = -5 for another line.

Let the equation of the line be y = mx + c

This line passes through A(-2,3)

Therefore, 3 = -5(-2) + c

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Hence, equation of line is y = -5x - 7.

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kolezko [41]

Answer:

y=1/2x+1= A

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I hope this helps

Step-by-step explanation:

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1 year ago
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Answer:

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