Question 540859: a parabola passes through the points (0,8),(2,-1) and (4,-1). find the equation of the parabola.
thanks
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! a parabola passes through the points (0,8),(2,-1) and (4,-1).
find the equation of the parabola.
:
Using the form ax^2 + bx + c = y
The first point, 0,8, indicates that c = 8
:
Write equations for the other two points
x=2, y=-1
4a + 2b + 8 = -1
4a + 2b = -1 -8
4a + 2b = -9
:
x=4, y=-1
16a + 4b + 8 = -1
16a + 4b = -9
:
multiply the 1st equation by -2, add to the 2nd equation
-8a - 4b = +18
16a + 4b = -9
---------------adding eliminates b, find a
8a = 9
a = 
a = 1.125
:
Find b
4a + 2b = -9
4(1.125) + 2b = -9
4.5 + 2b = -9
2b = -9 - 4.5
2b = -13.5
b = -6.75
:
The equation: y = 1.125x^2 - 6.75x + 8
:
You can confirm this by substituting for x and finding y for each point
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