SOLUTION: 16. Which quadratic rule represents the data in the table?
x -1,0,1,2,3
y 6,5,6,9,14 this is what the data looks like
y = –2x² + 5
y = –x² + 5
y = x² – 5
y = x² + 5
I
Algebra.Com
Question 878392: 16. Which quadratic rule represents the data in the table?
x -1,0,1,2,3
y 6,5,6,9,14 this is what the data looks like
y = –2x² + 5
y = –x² + 5
y = x² – 5
y = x² + 5
I think it is b
Found 2 solutions by solver91311, josgarithmetic:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Why do you think it is b?
If 
Then
\ =\ -(-1)^2\ +\ 5\ =\ -1\ +\ 5\ =\ 4)
\ =\ -(0)^2\ +\ 5\ =\ 0\ +\ 5\ =\ 5)
\ =\ -(1)^2\ +\ 5\ =\ -1\ +\ 5\ =\ 4)
\ =\ -(2)^2\ +\ 5\ =\ -4\ +\ 5\ =\ 1)
\ =\ -(3)^2\ +\ 5\ =\ -9\ +\ 5\ =\ -4)
So apparently b is incorrect.
Consider the standard form of a quadratic function:
If the point )
is an element of the solution set, then
^2\ +\ b(-1)\ +\ c)
must hold and
If the point )
is an element of the solution set, then
^2\ +\ b(0)\ +\ c)
must hold and
If the point )
is an element of the solution set, then
^2\ + b(1)\ +\ c)
must hold.
Simplfying:
Substituting
Solving by elimination:
and 
Substituting the now known values of a, b, and c into 
yields:
Checking the result:
\ =\ (-1)^2\ +\ 5\ =\ 1\ +\ 5\ =\ 6)
\ =\ (0)^2\ +\ 5\ =\ 0\ +\ 5\ =\ 5)
\ =\ (1)^2\ +\ 5\ =\ 1\ +\ 5\ =\ 6)
\ =\ (2)^2\ +\ 5\ =\ 4\ +\ 5\ =\ 9)
\ =\ (3)^2\ +\ 5\ =\ 9\ +\ 5\ =\ 14)
Looks right to me.
John
My calculator said it, I believe it, that settles it
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
That data shows a vertex at (0,5). Data also shows the vertex is a minimum. Coefficient on leading term must be greater than zero.
Comparing according to standard form equation should make the correct choice clear:
and .
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