Question

PLEASE HELP!!
MEDAL!!
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 be the score if a student does no homework?

Answer 1

begin by expanding the right side of the function

Answer 2

can you take it from here?

Answer 3

here is the corrected form

Answer 4

\[s(t) = -(t ^{2}-12t+36)+99=-t^2+12t+63\]

Answer 5

how did you get 63??

Answer 6

see the negative outside of the whole expression up there? ^^^^^
That means we get a -36, and a positive 99, which is equal to 63

Answer 7

get it?

Answer 8

yea but i dont know what to put on the questions which are a,b,and c

Answer 9

ok so for a, it asks for the maximum score. We get the maximum t value using -b/2a, which, in this case, is -12/-2, or 6. Therefore, if the guy studies 6 hours, he will have the highest grade possible. The exact grade, is obtained by plugging t=6 into the equation and getting s(6)=-36+72+63=99

Answer 10

the max hours is 6, the max grade is 99

Answer 11

if he doesnt do any studying, then t=0, so he gets a s(0)=63, or a gradeof 63

Answer 12

i dont really like this problem, because its confusing in that if he studies 8 hours, he gets a lower grade that if he studies 6, but nevertheless, your answers are above ^ ask any questions you have and please medal :)

Answer 13

can you also help me with this:
6x^2+24x=126 by factoring

Answer 14

bring all the factors to one side like so: 6x^2+24x-126=0

Answer 15

then, divide both sides by 6, to get x^2+4x-21=0

Answer 16

then factor this to (x+7)(x-3)=0

Answer 17

therefore x+7=0 or x-3=0, so your roots (answers) are x=3 or x=-7

Answer 18

is that what you needed?

Answer 19

yup thamks

Answer 20

no prob