Question

Help with quadratic! Really struggling with this

Answer 1

Explanation:

The equation

`G(h)=-3h^2+24h+47`

represents the grade you are going to earn which is represented by G(h) where h in the equation is the hours you study the week before.

Part A) Is totally up to you because in the question it asks What's the best possible grade you can earn with your current study habits lets say if you study around 4 hours the week before the test. Which means the value of h should be 4 because h represents hours in the equation.

so ,

`G(h)=-3h^2+24h+47\\G(4)=-3(4)^2+24(4)+47\\G(4)=-48+96+47\\G(4)=95\\`

So if you studied for 4 hours the week before the test you are going to score 95 marks which would be an A* grade.

Part B) In this part it asks you the maximum amount of study time you will need to have to earn that grade which means how many maximum hours you would need to earn a total of 95 marks which is 4.

Part C) The y-intercept is the constant in the equation in this case +47 is y-intercept and in the context of the problem it denotes that if you studied for 0 hours you would still earn 47 marks on the test, which would result you failing the test.

Part D) How many hours would you need to complete and still earn a zero would be:

`G(h)=-3h^2+24h+47\\-3h^2+24h+47=0`

because it says still earn a zero which means the grade is zero so now we solve the equation.

`-3h^2+24h+47=0\\3h^2-24h-47=0\\`

using the quadratic formula we get two values for h which are

h = 9.627 and h = -1.627 so eventually hours can never be in negative its impossible you can't study for -1.627 so our answer is 9.627 hours and you would still earn a zero after studying approximately 9.6 hours.

Part E) The grade that you will earn if you studied for 5 hours is:

`G(h)=-3h^2+24h+47\\G(5)=-3(5)^2+24(5)+47\\G(5)= -75+120+47\\G(5)=92\\`

You would earn 92 marks which would result in an A* grade

Answer 2

(A) 95

(B) h=4

(C) 47, represents 0 hours of study

(D) h=9.63

(E) 92

Explanation:

(A) They are asking for the maximum of the graph of the equation which can be found using the vertex formula:

`max= c-(b^2)/(4a)`

where 'a' is the coefficient of the first term, 'b' is the coefficient of the second term and 'c' is the third term.

So we have:

`max=47-((24)^2)/(4(-3)) = 95`

(B) To find the hours of study required to get 95 we need to set the equation equal to 95:

`-3h^2+24h+47=95`

which can be rewritten as:

`-3h^2+24h+47-95=0`

or

`-3h^2+24h-48=0`

When we solve for 'h' we get h = 4

Therefore, studying 4 hours gives us a grade of 95, which is the maximum score from the equation.

(C) The function G(h) is our y and h is our x values. To find the y intercept, x (which is h in the equation) must be set to 0 and solved for y. This is because the y intercept is at the point where x =0.

So we have:

`G(h)=-3(0)+24(0)+47\\ =0+0+47\\ =47`

This is when h=0 and therefore is represents the grade when 0 hours of studying is done.

(D) To find how many hours of study can still produce a grade of 0, we need to set the function equal to 0 and solve for h.

`-3h^2+24h+47=0\\`

This gives us two results when solved quadratically:

`h=-1.63` and
`h=9.63`

Obviously, time cannot be negative so the answer is 9.63 hours.

(E) If we study for 5 hours, h should be equal to 5.

So substituting 5 for h we get:

`-3(5)^2+24(5)+47=92`

So 5 hours of study affords us a grade of 92.

Hope that explains it.