Question 1040451
The form in which your first two examples are written are very convenient for the question.  Study these videos:
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<a href=https://www.youtube.com/watch?v=M8LGsQMwwj4"">Derive equation for parabola given focus and directrix; vertex at orign</a>
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<a href="https://www.youtube.com/watch?v=Wworlx39KfQ">Similar, but different orientation, and vertex not at origin</a>



Check this one for your last example:  <a href="https://www.youtube.com/watch?v=MD4AiN1Gsmc">how to change quadratic equation from general to standard form, allowing you to figure out how to graph</a>