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Alenkinab [10]
3 years ago
10

Find constants a and b so that the minimum for the parabola f(x)=x^2+ax+b is at the point (6,7)

Mathematics
1 answer:
Blizzard [7]3 years ago
4 0
To find the minimum, take the derivative of the function and equate to zero:

f(x) = y = x² + ax + b
dy/dx = 2x + a = 0
Substitute x =6:
a = -2x
a = -2(6)
a = -12

Then, substitute x = 6, y = 7 and a = -12 to find b.

7 = (6)² -12(6) + b
7 + 36 = b
b = 43

Thus, a = -12 and b = 43
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Given:

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Add or subtract like terms together.

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