To write the quadratic equation of the form \( f(x) = ax^2 + bx + c \) with \( c = 0 \), the equation simplifies to:
\[ f(x) = ax^2 + bx \]
We can use the points (3, 15) and (6, 12) to create a system of equations.
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Using the point (3, 15): \[ f(3) = 15 \implies a(3^2) + b(3) = 15 \] \[ 9a + 3b = 15 \quad \text{(Equation 1)} \]
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Using the point (6, 12): \[ f(6) = 12 \implies a(6^2) + b(6) = 12 \] \[ 36a + 6b = 12 \quad \text{(Equation 2)} \]
Thus, the system of linear equations that can be used to identify the coefficients \(a\) and \(b\) is given by:
\[ \begin{cases} 9a + 3b = 15 \ 36a + 6b = 12 \end{cases} \]
Among the response options, the correct one is:
9a + 3b = 15 and 36a + 6b = 12.