Function type: Quadratic, see solution. Function rule: - 2x^2+42x+470
Practice makes perfect
Since the data has equally-spaced inputs, we can check whether the data is linear by checking the first difference sequence.
The first difference sequence is not constant, so this data is not linear. Let's check the second difference sequence. This tells whether the data is quadratic or not.
Since the second difference sequence is constant, this data is quadratic. We do not have enough data to use either vertex form or intercept form of a quadratic equation, so we will solve a system of three equations.
We write the equations by substituting values from the table for x and y.
(I): 690=a(10)^2+b(10)+c
(II): 630=a(5)^2+b(5)+c
(III): 470=a(0)^2+b(0)+c
Because the third equation immediately simplifies to c=470, we can substitute it into remaining two equation.
630=a(5)^2+b(5)+c & (I) 690=a(10)^2+b(10)+c & (II)
