Find the quadratic function $y=a x^{2}+b x+c$ whose graph passes through the given points.
\[
(-1,-3),(3,-7),(-2,3)
\]
\[
y=
\]
Answer
\(\boxed{y=x^{2}-3x-1}\) is the quadratic function that passes through the given points.
Step 1 ：We are given three points (-1,-3), (3,-7), and (-2,3) and we need to find the quadratic function \(y=a x^{2}+b x+c\) that passes through these points.
Step 2 ：We substitute these points into the function to get three equations: \(a - b + c = -3\), \(9a + 3b + c = -7\), and \(4a - 2b + c = 3\).
Step 3 ：Solving these equations, we find that \(a = 1\), \(b = -3\), and \(c = -1\).
Step 4 ：Substituting these values into the quadratic function, we get \(y=x^{2}-3x-1\).
Step 5 ：\(\boxed{y=x^{2}-3x-1}\) is the quadratic function that passes through the given points.
