If the graph of y=ax^2+bx+c passes through the points(-1,12),(0,5) and (2,-3) find the value of a+b+c
Here's how we go about it. We know that the y-intercept occurs when x is 0. And that in a polynomial of this form, the constant is the y-intercept. We see that one point is (0,5), that means when x is 0, y is 5, this implies c = 5. Now we use the other two points to obtain simultaneous equations.
using (x,y) = (-1,12) we get
a - b + 5 = 12..................................(1)
using (x,y) = (2,-3) we get
4a + 2b + 5 = -3...............................(2)
Thus our equations are:
a - b = 7...........................(1)
4a + 2b = -8......................(2)
So
a - b = 7............................(1)
2a + b = -4.........................(3) which we get by equation(2)/2
Adding these equations we obtain
3a = 3................................(1)+(3)
so a = 1
since a - b = 7
=> b = -6
so the numbers are a = 1, b = -6 and c = 5