Chapter 4 - An Introduction to Functions - 4-3 Patterns and Nonlinear Functions - Practice and Problem-Solving Exercises - Page 250: 13

$y=4x^2$

Using the first coordinate, we see that the y-intercept is $(0,0).$ Then, notice that the y-coordinates of the next four terms when divided by $4$ equal the square of the x values. Using that we can write the rule $y=4x^2,$ which satisfies all of the points given.