The question says h= -5t^2-25t models a football being kicked in to the air. And asks for the roots. I found that the roots are -5 and 0. But the answer is 5 and 0. I know time can't be negative. But u can't just switch -5 to 5. Can you.?
You are correct. The function should be
h(t) = 25t - 5t^2
The -5t^2 term is due to the downward pull of gravity. The +25t indicates an initial upward velocity.
Parabola - 5 t ^ 2 - 25 t is concave downward.
That's why you get negative time.
You can switch - 5 to 5.
If you want to see graph go on:
w o l f r a m a l p h a . c o m
When page be open in rectangle type:
- 5 t ^ 2 - 25 t , t = 0 to - 5
and click option: =
You wil see graph
You are correct that time (t) cannot be negative in this context.
To find the roots of a quadratic equation, such as h = -5t^2 - 25t, we set the equation equal to zero and solve for t. In this case, we have:
-5t^2 - 25t = 0
Now, to solve the equation, we can factor out common terms:
t(-5t - 25) = 0
This gives us two possible solutions: either t = 0 or -5t - 25 = 0.
To solve the second equation, we can isolate t by adding 25 to both sides:
-5t = 25
Dividing both sides by -5, we obtain:
t = -5
So, we have two solutions: t = 0 and t = -5.
However, as you correctly mentioned, negative time doesn't make sense in this context. So, we discard the negative value and conclude that the root of the equation is t = 0. The answer you provided, 5 and 0, is likely the result of a sign error.
Therefore, the correct root is t = 0, indicating that the football hits the ground at time t = 0.