Adam kicks the football in his backyard. The path of the football when kicked can be represented by the quadratic function y = - 16{x^2} + 85x where x is the horizontal distance (in feet) and y is the height (in feet). How far does Adam kick the football? Express your answer as a decimal rounded to the nearest hundredth.

Question

anonymous · Answer

I don't normally give answers, but since this question is from 2 days ago, I think it's safe to do so.
1. The y-intercepts are where the football meets the ground.
2. This equation will have 2 roots or x-intercepts.
3. Plug in 0 for y to find the x-intercepts
$$0 = -16x^2 + 85x$$
4. Factor  - this one is easy since both terms have an x.
$$0 = x(-16x + 85)$$
5. Set each factor equal to 0 and solve for x.
0 = x or 0 = -16x+85
6. x = 0 is already solved. That is where the football started.
7. Subtract 85 from both sides.
-85 = -16x
8. Divide both sides by -16
$$-85 \div -16 = 5.3125$$
So, the football travelled 5.3125 feet (that is where it hit the ground the second time or the second x-intercept) but the question asks for the distance to be rounded to the nearest hundredth. So...
The football traveled 5.31 feet.

anonymous · Answer

I already tried that answer and for some reason it was wrong .

anonymous · Answer

Was any explanation given?

anonymous · Answer

If the question is asking for the distance of the arc, I have no idea how to find that.

anonymous · Answer

all it said was this when i got it wrong Use your graphing calculator to find the solution.

anonymous · Answer

Try this explanation. It is beyond my current knowledge, but it might be the answer to your question.

anonymous · Answer

I have no idea what that is !!

anonymous · Answer

What class are you taking?

anonymous · Answer

That page is a lesson from a calculus class. Perhaps a college level calculus. I'm not sure. I haven't done math like that in 20 years.

anonymous · Answer

noooo im not taking tht

anonymous · Answer

Best ask the teacher then. I'm curious about the answer. Would you share the teacher's response please?

anonymous · Answer

sure. I emailed him I will let you know when he replies !

anonymous · Answer

Thanks.