Asked by anonymous
Use a system of equations to find the equation of the parabola y = ax^2 + bx + c that passes through the points. Solve the system using matrices. Use a graphing utility to verify your result.
The points are (1,6), (4,3), (5,-2)
The points are (1,6), (4,3), (5,-2)
Answers
Answered by
Reiny
using (1,6) ---> 6 = a + b + c
using (4,3) ---> 3 = 16a + 4b + c
using (5,-2) ---> -2 = 25a + 5b + c
The 2nd minus the first: 15a + 3b = -3 or <b>5a + b = -1</b>
the 3rd minus the 2nd: <b>9a + b = -5</b>
Now subtract those last two:
4a = -4
a = -1
sub that into 5a + b = -1 to get b
then go into the very first one to get c
using (4,3) ---> 3 = 16a + 4b + c
using (5,-2) ---> -2 = 25a + 5b + c
The 2nd minus the first: 15a + 3b = -3 or <b>5a + b = -1</b>
the 3rd minus the 2nd: <b>9a + b = -5</b>
Now subtract those last two:
4a = -4
a = -1
sub that into 5a + b = -1 to get b
then go into the very first one to get c
Answered by
anonymous
@reiny thanks but how did you get 16a in 3 = 16a + 4b + c and 25a in -2 = 25a + 5b + c
Answered by
Reiny
your equation is y = ax^2 + bx + c
so in (4,3), x = 4, and y = 3
so 3 = a(4^2) + b(4) + c
same for the other points
so in (4,3), x = 4, and y = 3
so 3 = a(4^2) + b(4) + c
same for the other points
Answered by
anonymous
thanks, now i get it
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