Question

The Turnip God is the protector of turnips. While flying on a Sunday afternoon an evil bird sees a juicy turnip on the ground and dives toward it. The bird’s dive follows the path y = 0.5x^2-7x+24.5. Unfortunately for the bird, the Turnip God happens to be watching and casts a spell on the bird that will turn the bird into a rock. The spell travels along the path y=x-3 . Sometimes the spell doesn’t work properly so it may not turn the bird into a rock on the first hit. At what points (x,y) will the spell hit the evil bird?

Answer 1

Hey! Interesting problem, I like it! (;
So we'll need a graph ...

Answer 2

Here's the graph:

Answer 3

The blue line represents the bird trajectory and the red line the spell path

Answer 4

Assume Turnip God is in heaven. So, the spell comes from the top
and we can assume the bird comes from the left...

I've labeled it on the graph, here:

Answer 5

thanks

Answer 6

So I have a question for you, at what point (in the graph) will the spell hit the bird?

Answer 7

Do you see the green points on the graph above ^?
What can we say about them? What would happen in those points? @alli6106

Answer 8

the green points are 5,2 and 11,8

Answer 9

You're right! That's where the spell and the bird collide where the spell hit the
evil bird. The green points are (5,2) and (11,8) - Those are the points where the spell will hit the bird.

Answer 10

ok