Question

The graph of a line and and exponential intersect twice, once, or not at all. Describe the possible number of intersections of each of the following pairs of graph. Your solution to each part should include all of the possibilities and a quickly sketched example of each one. (Part 1)(SHOW WORK)
a. A line and a parabola

b. Two different parabolas

Answer 1

a) A line can intersect a parabola at 2 points, 1 point, or no points respectively. The only possible way at which it intersects at 1 point, would be if it were tangent to the parabola. [Check first attachment]

b) Two different parabolas can intersect at 2 points, 1 point or no points respectively. [Check second attachment]

It is possible for 2 parabolas to intersect at 4 and even 3 points. But one of the parabolas would be on it's side. You can consider those cases.