Question

Explain the process that is used to transform a quadratic equation from standard form to vertex form

Answer 1

See below.

Explanation:

To convert a standard form quadratic of the form
`ax^2+bx+c=0`, subtract c from both sides.

`ax^2+bx+c = 0\\ax^2+bx = -c`

Now, complete the square by dividing b in 2 and squaring the result.

`(b)/(2)^2`

Add this term to both sides. Then write in factored form and subtract whats left on the other side of the equal side to the same side as the factored form. See example below:

`x^2 + 4x + 1 = 0\\x^2 + 4x = -1\\x^2 + 4x + 4 = -1+4\\(x+2)^2 = 3\\(x+2)^2 - 3 = 0`