 Hello and welcome to the session. In this session we will discuss a question which says that draw graph of the quadratic function 3 minus 4x minus x square and hence find the maximum value of the function. Now we will start with the solution. Here let y is equal to 3 minus 4x minus x square. Now for drawing a graph we will form a set of pairs of values for x and y. Now we have y is equal to 3 minus 4x minus x square. For x is equal to 0 y is equal to 3 minus 4 into 0 minus 0. This is equal to 3. Therefore for x is equal to 0 y is equal to 3. Now for x is equal to 1 y is equal to 3 minus 4 into 1 minus 1 square which is equal to 3 minus 4 minus 1 which is equal to minus 2. Therefore for x is equal to 1 y is equal to minus 2. Now for x is equal to 2 y is equal to 3 minus 4 into 2 minus 2 square. This is equal to 3 minus 8 minus 4 which is equal to minus 9. So therefore for x is equal to 2 y is equal to minus 9. For x is equal to minus 1 y is equal to 3 minus 4 into minus 1 minus of minus 1 whole square is equal to 3 plus 4 minus 1 which is equal to 6. So for x is equal to minus 1 y is equal to 6. For x is equal to minus 2 y is equal to 3 minus 4 into minus 2 minus of minus 2 whole square is equal to 3 plus 8 minus 4 which is equal to 7. So for x is equal to minus 2 y is equal to 7. For x is equal to minus 3 y is equal to 3 minus 4 into minus 3 minus of minus 3 whole square which is equal to 3 plus 12 minus 9 which is equal to 6. So for x is equal to minus 3 y is equal to 6. For x is equal to minus 4 y is equal to 3 minus 4 into minus 4 minus of minus 4 whole square which is equal to 3 plus 16 minus 16 which is equal to 3. So for x is equal to minus 4 y is equal to 3. For x is equal to minus 5 y is equal to 3 minus 4 into minus 5 minus of minus 5 whole square which is equal to 3 plus 20 minus 25 which is equal to minus 2. So for x is equal to minus 5 y is equal to minus 2. So we have formed a set of pairs of values for x and y and now we will plot these points on the graph. Now the coordinates of the first point is 0 3. So this is the point 0 3 on the graph. Now the coordinates of next point are 1 minus 2. So this is the point 1 minus 2 on the graph. Now the coordinates of next point are 2 minus 9. So this is the point 2 minus 9 on the graph. Similarly we will plot all these points on the graph. So now we have plotted all the points on the graph. Now by joining all these points we are getting a smooth curve and this curve is the required graph of the function. Now from the graph we can see that the highest point is A whose coordinates are minus 2 7. So we can write that the highest point on the graph is A whose coordinates are minus 2 7. Therefore the maximum value of the function is AL which is equal to 7. Hence the maximum value of the function is equal to AL which is equal to 7 which is attained at x is equal to minus 2. You can see from the graph that the maximum value of the function is AL which is equal to 7 and it is attained when x is equal to minus 2. So this is the solution of the given question and that's all for this session. Hope you all have enjoyed the session.