A parabola's equation can take two different forms. The first, vertex form, is represented as y= a(x-h)²+k, where x and y are the coordinates for individual points on the parabola, a is the scalar that can change the shape and direction of the parabola, and h and k are the vertex points. The parabola's standard form equation, represented as y = ax² + bx + c, focuses on the parabola's direction and its axis of symmetry, which is the line that bisects the parabola. Converting from the vertex to the standard form can make the equation more compatible for other calculations.
Square the portion of the equation under the exponent. For example, if the vertex form of the equation is y = 2(x + 3)² + 4, then squaring the part of the equation under the exponent would result in y = 2(x² + 6x +9) + 4.
Multiply the coefficient in front of the parentheses to the portion of the equation inside the parentheses. For the example, multiplying 2 to (x² + 6x +9) results in 2x² + 12x +18, resulting in the equation y = 2x² + 12x +18 + 4.
Combine like terms in the equation. Like terms are those terms which either contain the same variable and have the same power applied to the variable. For the example, the only like terms of the equation are the constants 18 and 4. Combining those terms results in the equation y = 2x² + 12x +22. This is the standard form of the parabola's equation.