Write the quadratic function $f(x)=x^{2}-42 x-46$ in the form $f(x)=(x-h)^{2}+k$
\[
f(x)=
\]

Step 1 ：Given the quadratic function $f(x)=x^{2}-42 x-46$

Step 2 ：Rewrite the function in the form $f(x)=(x-h)^{2}+k$

Step 3 ：First, find the value of $h$ using the formula $h = -\frac{b}{2a}$

Step 4 ：Substitute $a = 1$ and $b = -42$ into the formula to get $h = 21$

Step 5 ：Next, find the value of $k$ by substituting $h$ into the function $f(h)$

Step 6 ：Substitute $h = 21$ into the function to get $k = -487$

Step 7 ：Finally, rewrite the function in vertex form using the values of $h$ and $k$

Step 8 ：Substitute $h = 21$ and $k = -487$ into the vertex form to get $f(x)= (x-21)^{2}-487$

Step 9 ：\(\boxed{f(x)= (x-21)^{2}-487}\) is the quadratic function in the form $f(x)=(x-h)^{2}+k$