SOLUTION: please use the standard from of a parabola given by {{{y=ax^2+bx+c}}} to write an eqaution of a parabola that passes through the given points
(1,2)(-1,-6) and (2,-3)
Question 331817: please use the standard from of a parabola given by to write an eqaution of a parabola that passes through the given points
(1,2)(-1,-6) and (2,-3) Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! use the standard from of a parabola given by y = ax^2 + bx + c to write an
equation of a parabola that passes through the given points,
(1,2)(-1,-6) and (2,-3)
:
Write an equation for each pair
:
x=1; y=2
a(1^2) + b(1) + c = 2
a + b + c = 2
:
x=-1; y=-6
a(-1^2) + b(-1) + c = -6
a - b + c = -6
:
x=2; y=-3
a(2^2) + b(2) + c = -3
4a + 2b + c = -3
:
Subtract the 2nd equation from the 1st equation
a + b + c = 2
a - b + c = -6
-----------------subtracting eliminates a & c, find b
2b = 8
b = 4
:
Replace b in the 1st equation
a + 4 + c = 2
a + c = 2 - 4
a + c = -2
:
replace b in the 3rd equation
4a + 2(4) + c = -3
4a + c = -3 - 8
4a + c = -11
:
Use elimination with these two equations
4a + c = -11
a + c = -2
------------------subtraction eliminates c, find a
3a = -9
a = -3
:
Find c using the 1st equation
-3 + 4 + c = 2
1 + c = 2
c = 2 - 1
c = 1
:
The equation: y = -3x^2 + 4x + 1
:
check by replacing x and finding y for each given pair
