Write the equation of the parabola that passes through the points \( (-7,-7),(-5,0) \), and \( (-2,0) \). 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.

To write the equation of the parabola in the form \( y = a(x - p)(x - q) \), we first identify the roots of the parabola. The points \( (-5, 0) \) and \( (-2, 0) \) indicate that the roots \( p \) and \( q \) are \( -5 \) and \( -2 \), respectively. Thus, we can start with the expression: \[ y = a(x + 5)(x + 2) \] Next, we need to find the value of \( a \) using the third point \( (-7, -7) \). We substitute \( x = -7 \) and \( y = -7 \) into the equation: \[ -7 = a(-7 + 5)(-7 + 2) \] \[ -7 = a(-2)(-5) \] \[ -7 = 10a \] \[ a = -\frac{7}{10} \] Now, we can write the full equation of the parabola: \[ y = -\frac{7}{10}(x + 5)(x + 2) \] This is the equation of the parabola passing through the given points.