<PRE><B>Question 535713</B>
y=(a(x-h)^2) + k is vertex form.  The vertex is (h,k).  +a is smiley, -a is frowney - that tells you if the parabola opens up or down.  To convert an equation to vertex form complete the square.&lt;P&gt;

y=x^2+6x+4&lt;P&gt;
Step 1:  move the loose number (the constant term) to the y side.&lt;P&gt;
y-4=x^2 + 6x&lt;P&gt;
Step 2:  Factor out whatever multiplies x^2.  Here it&#39;s 1, so this step does nothing except place the right side in ()&#39;s.&lt;P&gt;
y-4=(x^2 + 6x)&lt;P&gt;

Step 3:  Make a space after the constant on the y side, place the factor before x^2 before that space and the sign before that space is the same as the sign of the number in front of x^2.  Again, since it&#39;s 1, no need for that part.&lt;P&gt;
y-4+()=(x^2 + 6x)&lt;P&gt;
Take 1/2 the coefficient of the x term (the number in front of x).  Remember its sign.  Square it.  Add it to both sides inside the ().&lt;P&gt;
y-4+(9)=(x^2 + 6x +9)&lt;P&gt;
Multiply out the &quot;a times the squared coefficient&quot; part on the left-hand side (remember, in this one a = 1 so that does nothing), and convert the right-hand side to squared form. (This is where you use that sign you kept track of earlier, putting that sign in the middle of the squared expression.)&lt;P&gt;
y-4+(9)=(x+3)^2&lt;P&gt;
Simplify - combine like terms.&lt;P&gt;
y+5=(x+3)^2&lt;P&gt;
Move the constant term from the right back to the left.&lt;P&gt;
y=(x+3)^2 - 5&lt;P&gt;
Write in vertex form y=(a(x-h)^2) + k.  In other words if the squared term is x+h write it as x-(-h).  If the k term is negative, write it as + (-k).&lt;P&gt;
y=(x-(-3))^2  + (-5)&lt;P&gt;
Now the values for h and k are clear.&lt;P&gt;
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follow an example, but even better if you understand the concept.&lt;/B&gt;&lt;P&gt;</PRE>