Question

How to change standard form to vertex form of a parabola?

Answer 1

Step 1: Different forms of equations of parabola:

The standard form of a parabola is $\mathrm{y}={\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}$

Vertex form of parabola is $\mathrm{y}=\mathrm{a}{(\mathrm{x}-\mathrm{h})}^2+\mathrm{k}$

$(\mathrm{h},\mathrm{k})$ represents the vertex of the parabola.

If $(\mathrm{a}<0)$ then parabola has the maximum value at $(\mathrm{h},\mathrm{k})$.

if $\left(\mathrm{a}>0\right)$ then parabola has the minimum value at $(\mathrm{h},\mathrm{k})$.

Step 2: Calculation of vertex form:

Compare the standard and vertex forms and use the below formulas to get the vertex form of a parabola.

$\mathrm{h}=\frac{-\mathrm{b}}{2\mathrm{a}},\mathrm{k}=\frac{-\mathrm{D}}{4\mathrm{a}}[\mathrm{D}={\mathrm{b}}^2-4\mathrm{ac}]$

Hence, we can find the vertex form of a parabola using the above method.