If you plot this, you can see the line somewhat resembles a parabola...or quadratic equation. So we can use the formula y=ax^2+bx+c.

We can set up three equations by plugging in x values and y values.

(0, 4); 4=a(0)^2+b(0)+c

(1,9); 9=a(1)^2+b(1)+c

(2,16); 16=a(2)^2+b(2)+c

Now with these equations we want to get rid of some of the variables. In the first equation we see that a & B are being multiplied by 0 and we are just left with 4=c. We can plug that into the other equations.

(0, 4); 4=c

(1,9); 9=a(1)^2+b(1)+4

(2,16); 16=a(2)^2+b(2)+4

Now we are left with two variables and we can use elimination to solve for each. Let's solve for b first.

-36=-4a-4b-16 <-----(multiply [9=a+b+4] by -4)

__+ 16=__ __4a+2b+4__

-20=-2b-12 <----(solve for b and you get 4)

If we plug 4 into either (1,9)'s or (2,16)'s equation we can solve for a and get our equation

9=a(1)^2+4(1)+4

9=a+4+4

9=a+8

1=a

Our equation:

y=x^2+4x+4