Question 1100969
<br>Vertex form is
{{{y = a(x-h)^2+k}}}<br>
The vertex is at (h,k); the parabola opens upward if a>0 or downward if a<0.<br>
You need to complete the square in x in order to be able to write the equation in that form.<br>
Note the leading coefficient of 1 makes this example easier; we know immediately that the coefficient a in the vertex form is 1, so we can ignore it.  Then
{{{y = x^2+16x+74}}}
{{{y = (x^2+16x) + 74}}}
{{{y = (x^2+16x+64) + 74 - 64}}}  [complete the square; half of 16 is 8; 8 squared is 64.  Then since you added 64 inside the parentheses you need to subtract 64 outside]
{{{y = (x+8)^2+10}}}<br>
This is vertex form.  The vertex (minimum value of the function) is at (-8,10).