 Hello and welcome to this session. In this session we will discuss a question that says that identify the axis of symmetry and the vertex for the given functions. Also compare the graphs of the functions and the functions are given to us as y is equal to minus 2 x square and y is equal to minus 2 into x minus 5 whole square plus 5. Now let us start with the solution of the given question. Now we are given two quadratic functions y is equal to minus 2 x square and y is equal to minus 2 into x minus 5 whole square plus 5. Now we know that equation of quadratic function in vertex form is given by y is equal to a into x minus h whole square plus k, where periods of vertex are given by axis of symmetry in finite equation x is equal to, now here both of these functions are in vertex form. Now the first quadratic function is given to us as y is equal to minus 2 x square. It can be written as y is equal to minus 2 into x minus 0 whole square plus 0. Now comparing it with the vertex form we have h is equal to 0 and k is equal to 0. Now we know that coordinates of vertex are given by hk, so here as h is equal to 0 and k is equal to 0. So vertex has coordinates 0 0 is given by an equation x. So for this quadratic function axis of symmetry will be given by the equation x is equal to 0. Thus y axis is axis of symmetry. Now let us consider the second quadratic function. Now comparing this function with the vertex form we have h is equal to and k is equal to 5. Therefore coordinates of vertex are given by 5 and axis of symmetry. For this quadratic function is given by the equation x is equal to 5 c in both the functions which is less than 0 thus graph of both the functions will open downward but the vertices will be different. Now let us see graphs of both the functions. Now here we have drawn the graphs of these two functions. Now of the function y is equal to minus 2 into x minus 5 whole square plus 5 the function y is equal to minus 2 x square in downward but the graph of the function y is equal to minus 2 x square has vertex 0 0 that is origin symmetry is y axis whose equation is given by x is equal to 0. Now the quadratic function y is equal to minus 2 into x minus 5 whole square plus 5 has vertex 5 5 the equation x is equal to 5 the graph of both the functions will open downward but the vertices will be different. Thank you for giving question and that's all for this session hope you all have enjoyed this session.