1)Draw the graph of Y=11+8x -2xx from x= -2 to x=+6.
2)from the graph find :
1)the approximate roots of the equation 2xx -8x -11=0.
2)the maximum and minimum value of Y.
3)the line of symmetry.
To draw the graph of Y = 11 + 8x - 2x^2 from x = -2 to x = 6, we can plot several points and then connect them.
We start by substituting values of x into the equation to find corresponding y-values:
For x = -2, Y = 11 + 8(-2) - 2(-2)^2 = 11 - 16 - 8 = -13
So, we have the point (-2, -13).
For x = -1, Y = 11 + 8(-1) - 2(-1)^2 = 11 - 8 - 2 = 1
So, we have the point (-1, 1).
For x = 0, Y = 11 + 8(0) - 2(0)^2 = 11 + 0 - 0 = 11
So, we have the point (0, 11).
For x = 1, Y = 11 + 8(1) - 2(1)^2 = 11 + 8 - 2 = 17
So, we have the point (1, 17).
For x = 2, Y = 11 + 8(2) - 2(2)^2 = 11 + 16 - 8 = 19
So, we have the point (2, 19).
For x = 3, Y = 11 + 8(3) - 2(3)^2 = 11 + 24 - 18 = 17
So, we have the point (3, 17).
For x = 4, Y = 11 + 8(4) - 2(4)^2 = 11 + 32 - 32 = 11
So, we have the point (4, 11).
For x = 5, Y = 11 + 8(5) - 2(5)^2 = 11 + 40 - 50 = 1
So, we have the point (5, 1).
For x = 6, Y = 11 + 8(6) - 2(6)^2 = 11 + 48 - 72 = -13
So, we have the point (6, -13).
Now, we can plot these points on the graph and connect them.
To find the approximate roots of the equation 2x^2 - 8x - 11 = 0 from the graph, look for the x-coordinates where the graph intersects the x-axis. From the graph, it appears that the approximate roots are x ≈ -1 and x ≈ 5.
To find the maximum and minimum values of Y, look for the highest and lowest points on the graph. From the graph, we can see that the maximum value of Y is approximately 19 and the minimum value of Y is approximately -13.
The line of symmetry can be found by identifying the vertical line that divides the graph into two symmetric halves. From the graph, it appears that the line of symmetry is x = 3.