Question

A student has learned that test scores in math are determined by this quadratic function: s(t) = -(t-6)^2 + 99

In the function, s is the score and t is the number of hours that a student spends on homework each week.

a. How many hours must a student spend on homework to achieve maximum score?

b. What is the maximum score?

c. Based on the function, what will the score be if the student does no homework?

Answer 1

a. 6, b. 99, c. 63

Explanation:

A) The function s(t) is in the vertex form. The standard vertex form is a(x-h)+k where the vertex is (h,k). The vertex is the highest (or lowest in some cases) point of the graph, so if we use s(t) to get the vertex we get that h=6 and k=99. This means that for a student to get a perfect score they need to study 6 hours

B) We can just take the k value from the first question because that's the highest value for s(t), so the highest score will be 99

C) For this one just plug in 0 for time, so -(0-6)^2+99. This equals -(-6)^2+99, which equals 99-36 =63