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

Algebra ->  Algebra  -> Inequalities -> 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       Log On

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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(13823) About Me  (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.
+graph%28+300%2C+300%2C+-4%2C+16%2C+-10%2C+40%2C+30.25-%28x-5.5%29%5E2%29+
The x coordinate of the vertex (maximum value) is midpoint between 5 and 6 or 5.5.
The equation has the form
A-k=a%28L-h%29%5E2
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)
A-k=a%28L-5.5%29%5E2
10-k=a%2810-5.5%29%5E2
1.10-k=20.25a
18-k=a%289-5.5%29%5E2
2.18-k=12.25a
Subtracting eq.2 from eq. 1 gives
10-k-%2818-k%29=20.25a-12.25a
-8=8a
a=-1
Using that value in 1.
1.10-k=20.25a
10-k=20.25%28-1%29
k=20.25%2B10
k=30.25
Your equation then becomes
A-k=a%28L-h%29%5E2
A-30.25=-%28L-5.5%29%5E2 or
A=30.25-%28L-5.5%29%5E2
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