Final answer:
To catch the fly at (5,17), the chameleon should be situated at (5,16), which is one unit directly below the fly when shooting its tongue straight out.
Step-by-step explanation:
The question asks to find the chameleon's point of timing to shoot its tongue to catch a fly situated at (5,17) when the parabolic equation is f(x)=x²-2x+3. To find the point of aim, we can substitute x=5 into the equation to find the y-coordinate at that x position. Since the chameleon needs to intercept the fly, the y-coordinate of the chameleon when its tongue is shot out should match that of the fly's current position. Therefore, substituting x=5 into f(x), we get:
f(5) = (5)² - 2(5) + 3 = 25 - 10 + 3 = 18
However, since the fly is at the point (5,17), the chameleon's position should be directly below the fly, as the tongue shoots straight out. We find the chameleon is one unit too high, so it must adjust to the point (5,16) to catch the fly.