Part A:<span>
</span><span>
<span>
<span>
<span>
<span>
<span>
<span>
<span>
<span>
<span>
<span>
<span>
<span>
<span>
</span></span></span></span></span></span></span></span></span></span></span></span>
<span>
</span></span></span><span>
</span><span>
The first thing of completing the square is writing the
expression </span><span>
</span> as <span>
</span> which expands to <span>
</span>.<span>
We have the first two terms exactly alike with the function
we start with: </span><span>
</span>and <span>
</span> but we need to add/subtract from the last term, 49, to
obtain 41. <span>
So, the second step is to subtract -8 from the expression </span><span>
</span><span>
The function in finalizing the square form is
</span><span>
</span><span>
Part B:
The vertex is acquired by equating the expression in the
bracket from part A to zero
</span><span>
</span><span>
</span><span>
</span><span>
It means the curve has a turning point at x = -7
This vertex is a minimum since the function will make a
U-shape.
A quadratic function </span><span>
</span> can either make U-shape or ∩-shape depends on the
value of the constant <span>
</span> that goes with <span>
</span>. When <span>
</span> is (+), the curve is U-shape. When <span>
</span> (-), the curve is ∩-shape<span>
Part C:
The symmetry line of the curve will go through the vertex,
hence the symmetry line is </span><span>
</span><span>
<span>This function is shown in the diagram below</span></span>
