SOLUTION: ): HI! please help me with this.......... length , area 10 , 10 9 , 18 8 , 24 7 , 28 6 , 30 5 , 30 4 , 28 3 , 24 2 , 18 1 , 10 graph this and explain whether

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Question 108620: ): HI!
please help me with this..........
length , area
10 , 10
9 , 18
8 , 24
7 , 28
6 , 30
5 , 30
4 , 28
3 , 24
2 , 18
1 , 10
graph this and explain whether we can connect or not connect points
ps.
i think the equation is
L^2+11 and if i am wrong please correct me

Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
Yes, you can connect the dots.
Graphing the points you see that it is a parabola opening downward.

The x coordinate of the vertex (maximum value) is midpoint between 5 and 6 or 5.5.
The equation has the form

where (h,k) are the (x,y) coordinates of the vertex.
We need to solve for a and k.
Use two values for (L,A) that you have: (10,10) and (9,18)


1.

2.
Subtracting eq.2 from eq. 1 gives



Using that value in 1.
1.



Your equation then becomes

or

Check your answers.
A(10)= 10
A(9) = 18
A(8) = 24
A(7) = 28
A(6) = 30
A(5) = 30
A(4) = 28
A(3) = 24
A(2) = 18
A(1) = 10
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