find real numbers a,b,c so that the graph of the function y=ax^2+bx+c contains the points (-11,4), (2,3) , and (0,1)
Write three equations, with each point in one. Then solve the three equations.
To find the real numbers a, b, and c, we can substitute the given points into the equation y = ax^2 + bx + c to form a system of three equations.
Let's write the equations using the points (-11,4), (2,3), and (0,1):
1. For the point (-11, 4):
4 = a(-11)^2 + b(-11) + c
2. For the point (2, 3):
3 = a(2)^2 + b(2) + c
3. For the point (0, 1):
1 = a(0)^2 + b(0) + c
Now we have three equations:
1. 4 = 121a - 11b + c
2. 3 = 4a + 2b + c
3. 1 = c
We can now solve this system of equations to find the values of a, b, and c.