Since the directrix is vertical, use the equation of a parabola that opens up or down.

The vertex <math><mstyle displaystyle="true"><mrow><mo>(</mo><mi>h</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></mstyle></math> is halfway between the directrix and focus. Find the <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> coordinate of the vertex using the formula <math><mstyle displaystyle="true"><mi>y</mi><mo>=</mo><mfrac><mrow><mtext>y coordinate of focus</mtext><mo>+</mo><mtext>directrix</mtext></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> . The <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> coordinate will be the same as the <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> coordinate of the focus.

Simplify the vertex.

Subtract <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> .

Divide <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

The distance from the focus to the vertex and from the vertex to the directrix is <math><mstyle displaystyle="true"><mrow><mo>|</mo><mi>p</mi><mo>|</mo></mrow></mstyle></math> . Subtract the <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> coordinate of the vertex from the <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> coordinate of the focus to find <math><mstyle displaystyle="true"><mi>p</mi></mstyle></math> .

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

Substitute in the known values for the variables into the equation <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mi>h</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>4</mn><mi>p</mi><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mi>k</mi><mo>)</mo></mrow></mstyle></math> .

Simplify.

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