Answer:
the standard form of a quadratic equation is ax² + bx + c
the vertex form is a(x - h) + k where <em>h</em> & <em>k </em>are the x and y coordinates
to get from standard form to vertex form, you would have to follow this formula to find <em>h:</em>
-b/2a
plug in the values, and you will get the value of <em>h. </em>
to get <em>k,</em> you plug in the value you have just found in the above formula into the original equation, and that is the value of <em>k. </em>
the <em>a</em> in the vertex form is the value of <em>a</em> 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 <em>x</em> is
(-1)² + 2(-1) + 4 --> 1 - 2 + 4 = 3
we have both <em>h </em>and <em>k</em>, 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