Answer:
1. The function is -2x^2 + x + 3.
Step-by-step explanation:
1. The point at (1,2) gives the equation:
a * (1^2) + 1b + c = 2
a + b + c = 2
The point at (-2,-7) gives the equation:
a * (-2^2) + (-2b) + c = 7
4a - 2b + c = -7
The point at (2,-3) gives the equation:
a * (2^2) + 2b + c = -3
4a + 2b + c = -3
Hence, all three equations are:
a + b + c = 2
4a - 2b + c = -7
4a + 2b + c = -3
Now, subtract the second equation from the third equation to get:
(4a + 2b + c) - (4a - 2b + c) = -3 - (-7)
4a - 4a + 2b + 2b + c - c = -3 + 7
4b = 4
b = 1
Hence, let's now update our previous equations:
a + 1 + c = 2 => a + c = 1
4a - 2(1) + c = -7 => 4a + c = -5
4a + 2(1) + c = -3 => 4a + c = -5
This can be further whittled down into two equations:
a + c = 1
4a + c = -5
Hence, we can now subtract the first equation from the second to get:
(4a + c) - (a + c) = -5 - 1
4a - a + c - c = -6
3a = -6
a = -2
Therefore, c = 3 (a + c = 1, -2 + c = 1, c = 1 + 2, c = 3).
And the function is -2x^2 + x + 3.
Hope this helped!
