Finding the Domain and Range of a Quadratic Function

[n3w ton]

Question: Ryan is trying to hit a golf ball over a tree that is 18m above the ground. The height of the ball is modeled by the function h(t)= -5t² + 20t, where t is the time in seconds. Explain the domain and range of the function. Will the ball go over the tree?

This is grade 11 review and I totally forgot how to do this. (I think finding the max/min).

I need some help getting started in the right direction or even finding the answer of the domain (with steps please), and I will try to figure out the range my self.

I already know the answer's I need to know how to get them.

D: (XER | 0 < X <4)
R: (YER | 0 < Y <20)
Meaning the ball will pass over the tree.

But how did they get that! Please help.

 

[berkeman]

Question: Ryan is trying to hit a golf ball over a tree that is 18m above the ground. The height of the ball is modeled by the function h(t)= -5t² + 20t, where t is the time in seconds. Explain the domain and range of the function. Will the ball go over the tree?

This is grade 11 review and I totally forgot how to do this. (I think finding the max/min).

I need some help getting started in the right direction or even finding the answer of the domain (with steps please), and I will try to figure out the range my self.

I already know the answer's I need to know how to get them.

D: (XER | 0 < X <4)
R: (YER | 0 < Y <20)
Meaning the ball will pass over the tree.

But how did they get that! Please help.

One way to work on this problem is to graph that function, starting at time t=0. Keep plugging in 1 second increments to see what the general shape of the function is.

Have you had some differential calculus? If so, how do you find the max of that function? What can you say about the tangent to the curve at the maximum point of that graph?

 

[LCKurtz]

If you haven't had calculus write it as -5(t²-4t) and complete the square inside the parentheses. It will then be easy to see the range and answer the question.