 Hello and welcome to this session. In this session we will discuss a question which says that, what is the equation of qualitative function shown in graph? Now let us start with the solution of the given question. Now we have given the graph of an upward facing parabola with vertex having coordinates minus 1 minus 2 and a point 9 on this curve that is the point with coordinates minus 4, 14. Now we know that equation of qualitative function in vertex form is given by y is equal to a into x minus h whole square plus k where coordinates of vertex are given by h k now here is minus 1 and k is minus 2. So let us prove these values in vertex form of qualitative function. Now let this be equation 1 so that h is equal to minus 1 and k is equal to minus 2 in equation 1 we have y is equal to a into x minus of minus 1 whole square plus of minus 2 this implies y is equal to a into x plus 1 whole square minus 2. Now we have to find a, now we know that this point with coordinates minus 4, 13 lies on this curve which is the curve of qualitative function. So for finding the value of a we will put e to minus 4 and y is equal to 13 in this equation. Now let this be equation number 2. Now let us put x is equal to minus 4 and y is equal to 13 in equation 2. So we have 13 is equal to a into minus 4 plus 1 whole square minus 2. This implies 13 is equal to a into, now minus 4 plus 1 is minus 3 whole square minus 2. This implies 13 is equal to a into, now minus 3 whole square is 9 so it will be 13 is equal to 9a minus 2. Further this implies 13 plus 2 is equal to 9a which implies 15 is equal to 9a. Now we divide both sides of this equation by 9. So we have 15 upon 9 is equal to 9a upon 9 which implies now 3 into 3 is 9 and 3 into 5 is 15 and 9 into 1 is 9. So we have 5 upon 3 is equal to a or we can write it as a is equal to 5 upon 3. Now this is equation 2. Now we put a is equal to 5 upon 3 equation 2 and we have y is equal to 5 upon 3 into x plus 1 whole square minus 2. So this is the required equation of this quadratic function shown in graph. So this is the solution of the given question. That's all for this session. Hope you all have enjoyed this session.