To start with, be sure that your equation is in standard form. The standard form of a quadratic equation is:
y = Ax2 + Bx + D, where 'x' and 'y' are variables and 'A', 'B' and 'D' are integral constants. For instance, y = 4x2 + 12x – 90. The equation is in its standard form. Next we have to move the constant to the left side (by adding or subtracting it) of the equal sign. So our equation can now be written as: y + 90 = 4x2 + 12x.
On right side of equal sign as we can see that the terms are written the form of coefficients of powers of 'x', factor out 'u' which is the coefficient of squared term. In our equation, the coefficient of squared term is 4. Factoring it out leaves us with y + 90 = 4(x2 + 3x).
Next make the term in the parenthesis a perfect Square. This can be done as:
y + 90 = 4(x2 + 2 * (3/2) x + 9/4),
or y + 90 = 4(x + 3/2)2.
Now in last move the constant (on the left side of the equation) back to the right side. In the example, subtract 90 from both sides, giving y = 4(x + 3/2)2 - 90. The equation is now in vertex form with vertex given as is (-3/2, -90).