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Given the following function, what is the vertex?f(x) = -2|x - 3| + 4

User Manish R
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SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given function


f(x)=-2|x-3|+4

STEP 2: Find the vertex


\mathrm{Absolute\:value\:function\:vertex\:points\:are\:points\:where\:absolute\:values\:are\:zeros}

Equate the absolute value to zero to get the vertex


\begin{gathered} |x-3|=0 \\ x-3=0 \\ x=0+3=3 \end{gathered}

Substitute the value of x to get the y-value


\begin{gathered} f(x)=-2|x-3|+4 \\ x=3 \\ f(3)=-2(0)+4 \\ f(3)=0+4=4 \end{gathered}

Hence, the vertex of the given function is:


(3,4)

User Kafkaesque
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