Write the equation of the parabola that passes through the points \( (-3,0),(-2,-60) \), and \( (4,0) \). Write your answer in the form \( \mathrm{y}=\mathrm{a}(\mathrm{x}-\mathrm{p})(\mathrm{x}-\mathrm{q}) \), where \( \mathrm{a}, \mathrm{p} \), and q are integers, decimals, or simplified fractions. \begin{tabular}{|ll}\hline\( \square \) & \( (\square) \) \\ \hline\end{tabular}

To find the equation of the parabola that passes through the points \((-3,0)\), \((-2,-60)\), and \((4,0)\), we can use the fact that the parabola can be expressed in the form: \[ y = a(x - p)(x - q) \] where \(p\) and \(q\) are the x-coordinates of the roots (the points where the parabola intersects the x-axis). From the given points, we can see that the roots are \(-3\) and \(4\) since both points yield \(y = 0\). Thus, we can write: \[ y = a(x + 3)(x - 4) \] Next, we need to determine the value of \(a\). We can use the third point \((-2, -60)\) to find \(a\). Substituting \(x = -2\) and \(y = -60\) into the equation gives: \[ -60 = a(-2 + 3)(-2 - 4) \] This simplifies to: \[ -60 = a(1)(-6) \] So we have: \[ -60 = -6a \] Now, we can solve for \(a\): \[ a = \frac{-60}{-6} = 10 \] Now we can substitute \(a\) back into the equation of the parabola: \[ y = 10(x + 3)(x - 4) \] Thus, the equation of the parabola in the required form is: \[ \boxed{y = 10(x + 3)(x - 4)} \]