Answer:
The vertex from of the given function is \(f(x)=4(x+6)^2-134\).
Step-by-step explanation:
The given function is
\(f(x)=4x^2+48x+10\)
\(f(x)=4(x^2+12x)+10\)
If a expression is given as x²+bx, then add \((\frac{b}{2})^2\) in the expression to make it perfect square.
Here b=12, so add and subtract \((\frac{12}{2})^2\) in the parentheses.
\(f(x)=4(x^2+12x+6^2-6^2)+10\)
\(f(x)=4(x^2+12x+6^2)+4(-6^2)+10\)
\(f(x)=4(x+6)^2-4(36)+10\)
\(f(x)=4(x+6)^2-144+10\)
\(f(x)=4(x+6)^2-134\)
Therefore the vertex from of the given function is \(f(x)=4(x+6)^2-134\).
