Answer:
C
Step-by-step explanation:
Notice that the table doesn't have an exponential behaviour. Because an exponential function has the point (0,1), because all powers with a null exponent are equal to 1.
Also, notice that the table doesn't show a linear relation, because y-variable has all values positive.
Therefore, the only relation that follows the values of the table is
[tex]y=2.5x^{2}[/tex]
Let's evalue each x-value
[tex]y=2.5(-2)^{2} =2.5(4)=10\\y=2.5(-1)^{2}=2.5(1)=2.5\\ y=2.5(0)^{2}=2.5(0)=0\\y=2.5(1)^{2}=2.5\\y=2.5(2)^{2}=10[/tex]
Therefore, the right answer is C. The given values show a quadratic relation.
A faster way to deduct the quadratic pattern is observing that y-values are symmetric no matter if x-values are positive or negative, that meanst he function is pair, or quadratic.
