To find the <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> coordinate of the vertex, set the inside of the absolute value <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> . In this case, <math><mstyle displaystyle="true"><mi>x</mi><mo>=</mo><mn>0</mn></mstyle></math> .

Replace the variable <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> with <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> in the expression.

Simplify each term.

Remove non-negative terms from the absolute value.

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mfrac><mrow><mn>4</mn></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math> from <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

The absolute value vertex is <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mo>-</mo><mfrac><mrow><mn>4</mn></mrow><mrow><mn>5</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> .

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