This is not a linear function because the slope is varying. We know this because if we take two points and divide the difference between the y values by the difference between the x values we don't get the same value. Therefore there's no consistent slope. We could have a quadratic function of the form y=ax^2+bx+c. We find a, b and c, by substituting x and y values from the points we have and attempting to solve for a, b and c. When x=0, y=-2, so straight away we have c=-2. Our equation becomes y=ax^2+bx-2. Put x=1 and y=-1: -1=a+b-2, so a+b=1. Now we need another pair of values. Let's use x=y=2, so 2=4a+2b-2, and 4a+2b=4 or 2a+b=2. Substituting b=1-a we get 2a+1-a=2, so a=1 and therefore b=0. Our equation becomes y=x^2-2. Now we have to test if this fits the last point where x=3 and y=7. From the equation y=9-2=7. Bingo! It fits. So we have an equation that fits all the points: y=x^2-2.