table of values represents a linear, an exponential, or a quadratic function

Question

Tell whether the table of values represents a linear, an exponential, or a quadratic function.

x,y

(-2,-8)

(-1,-2)

(0,0)

(1,-2)

(2,-8)

The table of values represents what function listed above?

Write the function.

y=

Answer 1

the rules to follow are

linear [all y=mx+b] if y(x+1)-y(x)= constant for all x in table

exponential [of type y=a*b^x] if y(x+1)/y(x)=constant for all x in table

the table is not indicating linear or exponential.

the test for quadradic is harder (subtraction of subtractions is constant)

in this table have

-2-(-8)=6,,,0-(-2)=2,,,2-6=-4

-2-0=-2,,,,-8-(-2)=-6,,,-6-(-2)=-4

yay, it is quadradic

now f(x)=ax²+bx+c

when x=0 y=0 so c=0

when x=1 y=-2

-2=a+b

when x=-1 y=-2

-2=a-b

adding equations

2a=-4

a=-2 and b=0

Answer 2

This is a quadratic function because the shape of the graph resembles a parabola given the symmetry about the y-axis.

Specifically, the table of values represents the function y=-2x²