00:01
Hi, in this question we have to find the equation that represents the parabola passing through the point 2, -3, 5 ,3 and 7, -13.
00:12
Here we know that the parabola is represented by the equation y equal to ax square plus bx plus c.
00:34
Here we have to find the values of a, b and c such that here from the given points we can take it as x1 ,y1 equal to 2, -3, x2 ,y2 equal to 5 ,3 and x3 ,y3 equal to 7, -13.
00:54
Now we have to substitute all the values in the equation so that we will get at 2, -3 we will get the equation that 4a plus 2b plus c equal to minus 3.
01:10
Let us consider the equation as 1 and at 5 ,3 we will get 25a plus 5b plus c equal to 3.
01:22
This will be the second equation and at 7, -13 we will get minus 49a plus 7b plus c equal to minus 13 which is the third equation.
01:38
Now we have to solve this equation to find the values of a, b and c.
01:44
Now by solving 1 and 2 that is 4a plus 2b plus c equal to minus 3 and 25a plus 5b plus c equal to 3.
02:01
Here we have to solve this so that we will get minus 21a minus 3b equals to minus 6.
02:14
Let us consider the equation as 4.
02:16
Now we have to solve the equations 2 and 3.
02:19
Therefore by solving 2 and 3 we will have 25a plus 5b plus c equal to 3 then 49a plus 7b plus c equal to minus 13.
02:41
Now we have to subtract this so that we will get minus 24a minus 2b equals to 16.
02:55
This will be the fifth equation.
02:57
Now we have to solve 4 and 5...