EXPLANATION
The intercept-form of a quadratic function is as follows:
y = a(x - p)(x - q)
Now, as the roots are (-5,0)
Since the parabola passes through the point (−5,0), then 0=25a−5b+c
Since the parabola passes through the point (−1,0), then 0=a−b+c.
Since the parabola passes through the point (−7,−24), then −24=49a−7b+c.
Thus, we have obtained the following system:
Solving it we get that a=−2, b=−12, c=−10.
Thus, the equation of the parabola is y=(−2x−10)(x+1)
