SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given function
[tex]f(x)=-2|x-3|+4[/tex]STEP 2: Find the vertex
[tex]\mathrm{Absolute\:value\:function\:vertex\:points\:are\:points\:where\:absolute\:values\:are\:zeros}[/tex]Equate the absolute value to zero to get the vertex
[tex]\begin{gathered} |x-3|=0 \\ x-3=0 \\ x=0+3=3 \end{gathered}[/tex]Substitute the value of x to get the y-value
[tex]\begin{gathered} f(x)=-2|x-3|+4 \\ x=3 \\ f(3)=-2(0)+4 \\ f(3)=0+4=4 \end{gathered}[/tex]Hence, the vertex of the given function is:
[tex](3,4)[/tex]