Question 733982: Part of Sydney Harbor Bridge in Sydney,Australia can be modeled by a parabolic
arch. If the arch would pass through the points (0,23) (-5,2), (4,-40),write the
equation of the parabola to model the arch.
Please help me solve this
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Part of Sydney Harbor Bridge in Sydney,Australia can be modeled by a parabolic
arch.
If the arch would pass through the points (0,23) (-5,2), (4,-40), write the
equation of the parabola to model the arch.
:
Using the form, ax^2 + bx + c = y, find a, b, c
:
The first pair, 0,23; tells us that c = 23, find a and b with remaining pairs
-5,2
-5^2a - 5b + 23 = 2
25a - 5x = 2 - 23
25a - 5b = -21
:
4,-40
4^2a + 4b + 23 = -40
16a + 4b = -40 - 23
16a + 4b = -63
:
multiply the 1st equation by 4, and the 2nd equation by 5, and add them
100a - 20b = -84
80a + 20b = -315
------------------addition eliminates b, find a
180a = -399
a = -399/180
a = -2.2167
:
Find b using the 16a + 4b = -63
16(-2.21676) + 4b = -63
-35.467 + 4b = -63
4b = -63 + 35.467
4b = -27.533
b = -27.533/4
b = -6.883
:
The equation: y = -2.2167x^2 - 6.883x + 23; for the parabolic arch
:
Graphically
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