Answer:
A quadratic function.
[tex]y=2.5x^{2}[/tex]
Step-by-step explanation:
If you plot the points given in the table, you obtain the graph shown in the figure attached.
As you can see, it is a parabola, therefore, the function that best models the data is a quadratic function.
By definition, the parent function of a quadratic function is:
[tex]y=x^{2}[/tex]
You can compress or stretch it in the y-direction by multiplying the function by a constant [tex]C[/tex]:
[tex]y=Cx^{2}[/tex]
If [tex]0<C<[/tex], then the function is compressed.
If [tex]C>1[/tex], then the function is stretched.
You can find the constant of the function asked as following:
- Substitute x=1 into the parent function to obtain the y-coordinate:
[tex]y=(1)^{2}=1[/tex]
Then the point is (1,1)
- As you can see, with x=1 you obtain y=1 in the parent function, and in the function given in the table when x=1, y=2.5, therefore, the function is multiplied by 2.5. Therefore the constant is:
[tex]C=2.5[/tex]
Then the function is:
[tex]y=2.5x^{2}[/tex]
