Input the parabola's formula into your graphing calculator. For example, if the formula is y = 3x^2, type 3x^2 into the "y =" prompt.
Select "graph."
Determine the vertex simply by looking at the graph. The vertex is the point at which the two lines forming the parabola intersect. In the example used in Step 1, the vertex would be (0,0).
Input x-values into the parabola's formula and chart the results on graph paper. Begin with x = 0. Take the example from Section 1 (y = 3x^2). Inputting x = 0, you get 3(0^2) = 0, so the y-value is 0. Mark the point (0,0) on the graph.
Continue inputting x-values into the formula and charting the results on graph paper. Choose a few positive and a few negative numbers. You can use whole number increments (x = 1, x = 2, etc.) or fractional increments (x = 1/4, x = 2/4 or 1/2, etc.) for better accuracy.
Determine the vertex simply by looking at the graph. The vertex is the point at which the two lines forming the parabola intersect. In the example used in Step 1, the vertex would be (0,0).
Calculate the vertex algebraically by putting the equation for the parabola in the following form y = a(x-h)^2 + k. The point (h,k) is the vertex. For example, in the formula, y = 3(x-1)^2 + 4, the vertex is (1, 4). The constant "a" determines the orientation of the parabola (the direction in which it opens) but does not affect the vertex.
Complete the square to put an equation of the form y = ax^2 + bx + c into the form y = a(x-h)^2 + k. Start by squaring half of the coefficient of x and adding and subtracting it from the right side. Remember the coefficient is the number by which the variable is multiplied. For example, in the formula y = x^2 + 6x + 8, the coefficient of x is 6, so square 3 and add and subtract it from the right side to get y = x^2 + 6x + 8 + 9 - 9.
Rearrange the equation so you can complete the square: y = x^2 + 6x + 9 - 1, which simplifies to y = (x + 3)^2 - 1. Comparing this equation to y = a(x-h)^2 + k, you see that the vertex is (-3,-1). You can also deduce the orientation from a, which in this case is 1. A positive value for a indicates that the parabola opens upward; conversely, a negative value means it opens downward. To provide another example, in the formula y=2(x + 2)^2 + 4, a is 2, which means the graphs opens up, with the vertex at the bottom.