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.
