How do I identify a standard form and vertex form in a quadratic equation?

the standard form of a quadratic equation is ax² + bx + c

the vertex form is a (x - h) + k where h & k are the x and y coordinates

to get from standard form to vertex form, you would have to follow this formula to find h:

-b/2a

plug in the values, and you will get the value of h.

to get k, you plug in the value you have just found in the above formula into the original equation, and that is the value of k.

the a in the vertex form is the value of a in the standard form

so an example of this would be: x² + 2x + 4 where a = 1, b = 2 c = 4

to get this into vertex form we will use the formula - b/2a and solve:

-2/2 (1) - -> - 2/2 = - 1

now we plug in the value we found into the original equation wherever x is

(-1) ² + 2 (-1) + 4 - -> 1 - 2 + 4 = 3

we have both h and k, and we will put this into vertex form:

a (x - h) ² + k turns into - --> (x + 1) ² + 3

why x+1 and not x-1? the original equation has a negative sign, and the result we have is negative. this conflicts with the original equation and is therefore turned into a positive 1

where did a go? since a = 1, we do not need to write it, if a was equal to 2 then we would write the 2 in front