Question

Re-arrange this vertex equation y = 2 (x + 1)2 - 6 in standard form?

Answer 1

When we have a quadratic equation, we can have it in vertex and standard form.

The vertex form comes in the form:

$y=a\mleft(x-h\mright)^2+k$

The standard form comes in the form:

$y=ax^2+bx+c$

Converting to/from either simply requires some manipulations via expansion of the bracket as will be seen.

$\begin{gathered} y=2(x+1)^2-6 \\ y=2(x^2+2x+1)-6 \\ y=2x^2+4x+2-6 \\ y=2x^2+4x-4 \end{gathered}$

Hence, we have our standard form.