Problem

Given the quadratic function \(y = ax^2 + bx + c\) passes through the points (1,7), (2,11), (3,17), determine the constant of variation \(a\).

Answer

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Answer

Step 4: Solve for \(a\): \[a = \frac{6}{5}\]

Steps

Step 1 ：Step 1: Substituting the values from the points into the quadratic function gives us the following system of equations: \[\begin{align*} a + b + c &= 7, \quad (1) \\ 4a + 2b + c &= 11, \quad (2) \\ 9a + 3b + c &= 17. \quad (3) \end{align*}\]

Step 2 ：Step 2: Subtract equation (1) from equations (2) and (3). This will give us: \[\begin{align*} 3a + b &= 4, \quad (4) \\ 8a + 2b &= 10. \quad (5) \end{align*}\]

Step 3 ：Step 3: Subtract equation (4) from equation (5). This will give us: \[5a = 6\]

Step 4 ：Step 4: Solve for \(a\): \[a = \frac{6}{5}\]

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