From graphs to equations Write an equation of the following parabolas.

Solution 26EStep 1:In this problem we need to find the equation of parabola .The given graph is ; Definition of parabola ; A parabola is the set of all points in a plane that are equidistant from the focus and the directrix of the parabola.We know that , the equation of the standard parabola with its vertex at ( h , k) that opens downward is ; , where p is used to find the focus and directrix.Where , p is perpendicular distance from vertex to directrix.Therefore , p = =2 , since perpendicular distance from (, ) to ax+by+c =0 is d= .Hence , P= 2, and the given vertex is ( 0 , 2).Therefore , the equation of the standard parabola with its vertex at ( 0 , 2) that opens downward is ; That is , .