would you please give the graphical representation of the region bounded by the line y=x and the parabola y=x^2-6x-10?

h t t p : / / w w w . w o l f r a m a l p h a . c o m / i n p u t / ? i = y % 3 D x + a n d + y % 3 D x ^ 2 - 6 x - 1 0

..without the spaces~ :)

In google type:

functions graphs online

When you see list of results click on:

rechneronline.de/function-graphs/

In blue rectangle type: x^2-6x-10

In gray rectangle type: x

In Range x-axis from type -7 to 13

In Range y-axis from type -25 to 25

then click option Draw

Note that the two curves intersect at x = 2 and x = 5. You only need to evaluate the area intercepted between those points. It is the area between an inverted parabola and a 45 degree sloped straight line.

The area is easily calculated with calculus or numerical integration. The methods described by the previous two answers should get you the graph you want.

To graphically represent the region bounded by the line y=x and the parabola y=x^2-6x-10, you can follow these steps:

Step 1: Plot the intersection points:
To find the intersection points between the line y=x and the parabola y=x^2-6x-10, we need to set the two equations equal to each other:
x = x^2-6x-10

Rearranging the equation:
0 = x^2-7x-10

Now, we can solve this quadratic equation to find the x-values of the intersection points. We can factorize or use the quadratic formula to get the values of x, which are x = -2 and x = 5.

Step 2: Determine the boundaries of the region:
The boundaries of the region are the x-values of the intersection points we found. In this case, the boundaries are x = -2 and x = 5.

Step 3: Graph the line and the parabola:
Now, plot the line y=x and the parabola y=x^2-6x-10 on a coordinate plane, making sure to include the x-values of the boundaries. Additionally, add the intersection points (-2, -2) and (5, 5) on the graph.

Step 4: Shade the region:
Finally, shade the region between the line and the parabola that is bounded by the x-values -2 and 5.

The resulting graph will represent the region bounded by the line y=x and the parabola y=x^2-6x-10.