To find the equation of the parabola, first let's write the parent function,
y = a(x-h)^2+k. Ok, now we need to find the vertex and plug it in. Remember, (h,k). When we look at the problem the vertex is (0,4). Therefore we write it as y = a(x-0)^2 +4 or y = ax^2 + 4. Now we need to look to see if it was stretched or compressed. Keep in mind that on a normal parabola, if you move over 1 you go up one. If you move over 2 you go up four. If you move over 3, you go up 9. In this problem, you move over 1, you go up 1. If you move over 2, you go up 4. If you move over 3, you go up 9. From this information, we see that there is no stretch or compression. Therefore the equation of the graph shown is:
y= x^2 +4
