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