Answer:
y=2x^2+4x−16
Step-by-step explanation:
Assume that the equation of the parabola is y=ax2+bx+c.
Since the parabola passes through the point (−4,0), then 0=16a−4b+c.
Since the parabola passes through the point (2,0), then 0=4a+2b+c.
Since the parabola passes through the point (1,−10), then −10=a+b+c. Thus, we have obtained the following system:
{16a−4b+c=0; 4a+2b+c=0; a+b+c=−10
Solving it, we get that a=2, b=4, c=−16. Thus, the equation of the parabola is y=2x^2+4x−16.
