Parabolas - Write the Equation - Practice

How many parabolas have vertices with the same x-coordinate? And how many parabolas have the same vertex?

How many conditions do you need to uniquely determine the equation of a parabola?

You need to determine the equation of a parabola of the type . You know the coordinates of the vertex and of a point (distinct from the vertex) that lies on the graph of the parabola. Are these two conditions sufficient to uniquely determine the equation of the parabola?

You have all the main information about a parabola, except for its equation. Therefore, you know the coordinates of the vertex and the focus, the equations of the symmetry axis and the directrix, the points of intersection with the axes, and its concavity (whether it opens upward or downward). Write two exercises of the type "Determine the equation of a parabola of the form , given that..." and indicate the minimum number of conditions that are sufficient to determine the equation, choosing them from the data listed above. Then solve the exercises and find the equations of the parabolas you have defined.