Find the quadratic function $y=a x^{2}+b x+c$ whose graph passes through the given points.
\[
(-1,-9),(1,-3),(-2,-6)
\]

Answer

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Answer

$\boxed{y = 2x^{2} + 3x - 8}$

Steps

Step 1 ：Given three points (-1,-9), (1,-3), and (-2,-6), we need to find the quadratic function $y = ax^{2} + bx + c$ that passes through these points.

Step 2 ：Substitute these points into the function to get three equations: $a - b + c = -9$, $a + b + c = -3$, and $4a - 2b + c = -6$.

Step 3 ：Solve these equations to find the values of a, b, and c. The solution is $a = 2$, $b = 3$, and $c = -8$.

Step 4 ：Substitute these values into the quadratic function to get the final answer.

Step 5 ：$\boxed{y = 2x^{2} + 3x - 8}$

Find the quadratic function $y=a x^{2}+b x+c$ whose graph passes through the given points.\[(-1,-9),(1,-3),(-2,-6)\]

Answer

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Find the quadratic function $y=a x^{2}+b x+c$ whose graph passes through the given points.
\[
(-1,-9),(1,-3),(-2,-6)
\]