To find the coefficients \(a\) and \(b\) in the quadratic equation \(f(x) = ax^2 + bx + c\) with \(c = 0\), we will use the given points \((3, 15)\) and \((6, 12)\) in the equation for the function.
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Substitute the point \((3, 15)\): \[ f(3) = a(3^2) + b(3) + 0 = 15 \ 9a + 3b = 15 \quad \text{(Equation 1)} \]
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Substitute the point \((6, 12)\): \[ f(6) = a(6^2) + b(6) + 0 = 12 \ 36a + 6b = 12 \quad \text{(Equation 2)} \]
Now, we have the system of linear equations: \[ 9a + 3b = 15 \ 36a + 6b = 12 \]
The correct response is: "9a + 3b = 15 and 36a + 6b = 12."