 Hello and welcome to the session. In this session we will discuss a question which says that why the function that is this quadratic function given by y is equal to 2x square plus 12x plus 11 in vertex form, find its axis of symmetry and the vertex also find that what is the vertex is maximum or minimum point. Now the first part of the solution of this question, you should know horizontal and that is vertex form of quadratic function is given by y is equal to a into x minus h whole square plus k where areas of vertex are given by h k and axis of symmetry is given by equation x is equal to h. Now this result will work out as a key idea for solving out the given question. Now let us start with the solution of the given question. Now where we are given, quadratic function y is equal to 2x square plus 12x plus 11 and we have to write it in vertex form and from the key idea we know that vertex form of quadratic function is given by this equation find this, we will make its perfect square and write it in the form y is equal to a into x minus h whole square plus k. Now we have quadratic function y is equal to 2x square plus 12x plus 11. Now to make its perfect square in the first step we will make coefficients of x square 1. So here we will take from the writing side so it will be y is equal to 2 into x square plus 6x plus 11 by 2 the whole. Now here coefficient of x is 6 its half is equal to 1 by 2 into 6 that is equal to 3 and square of half the coefficient of x is equal to 3 square that is equal to 9. Now we will add and subtract square of half the coefficient of x that is 9 inside the bracket to make perfect square so we have y is equal to 2 into x square plus 6x plus 11 by 2 plus 9 minus 9 the whole. Now this implies y is equal to 2 into now here we will combine these three terms and it will be x square plus 6x plus 9 the whole and we will combine these three terms so it will be plus of 11 by 2 minus 9 the whole and this complete whole. Now this implies y is equal to 2 into x square plus 6x can be written as 2 into 3 plus 9 can be written as 3 square the whole plus now we are taking else here it will be 11 minus 18 whole upon 2 the whole and this complete whole. Now we know that a plus b whole square is equal to a square plus 2 ab plus b square and we will use this formula here so this implies y is equal to 2 into x plus 3 whole square plus of 11 minus 18 that is minus 7 upon 2 the whole and this complete whole and this implies now again we will open the brackets so it will be y is equal to 2 into x plus 3 whole square plus 2 into minus 7 upon 2 the whole further this implies y is equal to 2 into x plus 3 whole square minus 7 thus we have made it perfect square and this is the vertex form of the function. Now from the theory idea we know that this is the vertex form of quadratic function where all means of vertex are given by h k and x is of symmetry is given by the equation x is equal to h so here in this vertex form of the given quadratic function we have h is equal to minus 3 and k is equal to minus 7 and x is of symmetry given by the equation x is equal to h that is x is equal to minus 3 so coordinates of vertex are given by minus 3 minus 7 and x is of symmetry is given by the equation x is equal to minus 3 now everything see a is equal to 2 which is greater than 0 thus the graph of given function will open upwards and vertex is the minimum point so this is the solution of the given question that's all for this session hope you all have enjoyed this session.