The baseball team pitcher was asked to participate in a demonstration for his math class. He took a baseball to the edge of the root of the school building and threw it up into the air at a slight angle so that
the ball eventually fell all the way to the ground. The class determined that the motion of the ball from
the time it was thrown could be modeled closely by the function
h(t) =-161? + 64t + 80,
where h represents the height of the ball in feet aftert seconds.
a. Determine whether the function has a maximum value or a minimum value. Explain your answer
mathematically
B. Find the maximum or minimum value of the function. After how many seconds did the ball reach
this value? Show how you found your answers.
C. For what interval of the domain is the function increasing (i. e., ball going up)? For what interval of
the domain is the function decreasing (i. e., ball going down)? Explain how you know.
D. Evaluate h(0). What does this value tell you? Explain in the context of the problem.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

good luck on ur quiz test or homework. have a good day : )