How to convert vertex form to standard form

The vertex form and standard form of a parabola, where a parabola is a graph of a quadratic equation, are as follows:

Vertex Form: a (x - h) 2 + k, where (h, k) is the vertex of the parabola.

Standard Form: ax2 + bx + c

To convert from vertex form to standard form, we follow these steps.

In the expression a (x - h) 2 + k, FOIL out (x - h) 2 to get a (x2 - 2hx + h2) + k.

Distribute a throughout to get ax2 - 2ahx + ah2 + k.

Simplify the resulting expression.

For example, consider the parabola given in vertex form:

2 (x - 1) 2 + 3

To convert this to standard form, we follow our steps:

2 (x - 1) 2 + 3 FOIL out (x - 1) 2.

2 (x2 - 2x + 1) + 3 Distribute 2 through.

2x2 - 4x + 2 + 3 Simplify.

2x2 - 4x + 5 This is the parabola in standard form.

We see that 2 (x - 1) 2 + 3 in standard form is 2x2 - 4x + 5, and converting from vertex form to standard form can be done in a few easy steps.