If a quadratic polynomial curve in the shape of the semicircle is shown below. Then, the equation of this curve.
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Given : a quadratic polynomial curve in the shape of semicircle is shown below
To Find : the equation of this curve.
-x² + 2
x² + 2
x²/2 + 2
-x²/2 + 2
Solution:
Equation of the curve
y = ax² + bx + c
from the figure :
x = 2 , y = 0
x = -2 , y = 0
x = 0 and y = 2
=> 2 = 0 + 0 + c
=> c = 2
Hence y = ax² + bx + 2
=> 0 = 4a + 2b + 2
0 = 4a - 2b + 2
Adding both
=> 8a + 4 = 0
=> a = -1/2
on subtraction
4b = 0
=> b = 0
Hence y = -x²/2 + 2
the equation of this curve. is -x²/2 + 2
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Answer: -1/2x^2+2
Explanation:
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