Follow the formula. The function will appear f(x) = a(x-h)^2 + k. Take away number without an X next to it on each side of expression. For example, y = x^2 + 2x - 25. Subtract each side of the equation by -25. Therefore, you will have 0 = x^2 + 2x.
Determine what needs to be factored first. Using the example of f(x) = 2(x^2-4x) +7 you result with 2x^2 - 8x + 7. Then factor out the 2. After factoring out the 2 you will end up 2(x^2 - 4x + 4) + 7. Find two places where the X is equal to zero. You will need to factor what is left in the expression. This will appear as 0 = x (x +2) which will make x = 0 or -2.
Complete the square of the equation. From 2(x^2 - 4x + 4) + 7 will result (x^2 -4x) + 7 - 8.
Factor again and simplify. From (x^2 - 4x) +7 - 8, you will end up with 2 (x-2) -1.
Find the answer to the equation. The points to the vertex would be (2,-1) since 2 = x and -1 is the minimum value. Finally, since 2(x-2) -1 is more than or equal to 0, it shows that the parabola will open upward on the graph.