Finished:Math Practice Questions Bonus Question

A sequence is shown in the table below:

x = 1 , y =24

x = 2 , y =35

x = 3 , y =48

x = 4 , y =63

x = 5 , y =80

Find an equation that represents y, for any given x-value. Justify your answer by showing appropriate mathematical working.

Steps:

the gaps between them are 11, 13, 15, 17, which is a new sequence with gap of 2. meaning it's a Quadratic formula, assume y = ax^2+bx+c

because y'' = (2ax+b)'= 2a = 2 => a= 1 => y = x^2+bx+c

when x=1 => equation 1 : 1+b+c = 24

when x= 2 => equation 2 : 4+2b+c = 35

b,c can be solved by equation 2 minus equation 1 => 3 + b = 11 => b = 8

then put in equation 1 => c = 15

so y = x^2+8x+15

Answer: y = x^2+8x+15