A parabola passes through the points (0, −24), (−2, 0) and (4, 0). Find the equation of the parabola.

Given the pointin the first quadrant, find the downward opening parabola that passes through the pointand the origin such that the area under the parabola is minimum.

1. Find equations of both lines through the point that are tangent to the parabola

2. Show that there is no line through the point that is tangent to the parabola. Then draw a diagram to see why.

Find a parabola that passes through the point and whose tangent lines at and have slopes and, respectively.