Hi please help me with this ONE question from my Algebra homework. I have needed help for hours now. Please someone here please help me as soon as possible please

Question

Use finite differences or ratios to determine which parent function would best model the given data set.

A.) constant

B.) quadratic

C.) cubic

D.) linear

Answer 1

Clearly not constant...

slopes are not the same, no not linear either...

Ran it through the quadratic regression calculator online....

y = 7.625*x^2 - 21.5* x + 79.5

PERFECT FIT

Here is the linear algebra behind it:

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y = Ax^2+Bx+C is the quadratic function

Plugging in (6,225), (10,627) and (4,115.5) gives the 3 equations:

36A + 6B + C = 225

100A + 10B + C = 627

16A + 4B + C = 115.5

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eliminates C....

equation 2 MINUS equation 1:

64A + 4B = 402

16A + B = 100.5 <-- divides by 4

equation 2 MINUS equation 3:

84A + 6B = 511.5

14A + B = 85.25 <--- divides by 6

Subtracts these equations:

16A + B - (14A + B) = 100.5 - 85.25

2A = 15.25

A = 7.625

Then 14A + B = 85.25

14(7.625) + B = 85.25

solving for B, B = -21.5

Finally, per original 1st equation, since 36A + 6B + C = 225,

solving for C = 225 - 36A - 6B

= 225 - 36(7.625) - 6(-21.5)

= 79.5