Explain the steps necessary to convert a quadratic function in standard form to vertex form.
plz I need help

Answer :

Vertex form

a { ( x + b/2a )^2 - ( b/2a)^2 } + c

We are given than a quadratic function in standard form

ax^2 + bx + c

We have to explain steps which is necessary for converting quadratic x function in standard form to vertex form
We are explaining steps for converting a quadratic function into vertex form with the help of example

Suppose we have a quadratic function

2x^2 + x - 1

Taking 2 common from the given function the we get

2( x^2 + x/2 ) - 1

Now, we convert the equation of the form

2{ (x)^2 + 2 x x x1/4 + 1/16 - 1/16 } - 1
2{ ( x + 1/4)^2 - 1/16 } - 1
2{ ( x + 1/4 )^2 - (1/4)^2 } - 1

Vertex form = 2{ ( x + 1/4 )^2 - (1/4)^2 } - 1

Hence , the vertex form =

a { ( x + b/2a )^2 - ( b/2a )^2 } + c