To write a quadratic equation in vertex form, we typically need to know the values of [tex]\( h \)[/tex] and [tex]\( k \)[/tex] in the general vertex form equation, which is:
[tex]\[
y = a(x - h)^2 + k
\][/tex]
In your equation:
[tex]\[
y = 8(x + \square)^2 + \square
\][/tex]
It appears that the quadratic is already mostly in vertex form, but with blanks where specific values should be.
The standard vertex form we use is dependent on [tex]\( (x - h) \)[/tex], but we have [tex]\( (x + \square) \)[/tex]. To align with the typical notation of [tex]\( (x - h) \)[/tex]:
[tex]\[
y = 8(x - (-\square))^2 + \square
\][/tex]
From this, we see that [tex]\( h \)[/tex] corresponds to [tex]\( -\square \)[/tex] and [tex]\( k \)[/tex] still corresponds to the blank. If we denote these missing values as [tex]\( h \)[/tex] and [tex]\( k \)[/tex]:
[tex]\[
y = 8(x - h)^2 + k
\][/tex]
Therefore, the vertex form of the given equation is:
[tex]\[
y = 8(x - h)^2 + k
\][/tex]
Where [tex]\( h \)[/tex] is [tex]\(-\square\)[/tex] and [tex]\( k \)[/tex] is the last [tex]\(\square\)[/tex]. This form of the equation clearly shows the vertex [tex]\((h, k)\)[/tex] of the parabola.
