Lesson video
In progress...Loading...
Hi, I'm Miss Davies.
In this lesson, we're going to be using cubic graphs to solve equations.
The graph that is shown is of y is equal to x cubed + 2x.
We are being asked to use this graph to estimate the solution to x cubed + 2x is equal to 10.
If we compare these two equations, we can see that we have got one, this is equal to 10, and one where the left-hand side is identical to the equation above, but the right-hand side is equal to y.
This means we're going to draw the graph of y is equal to 10.
We can see that there is a point of intersection.
By drawing a line down, we can read the approximate x-value.
This is 1.
8, meaning that x is approximately equal to 1.
8.
Again, we have been given the graph of the function y is equal to x cubed + 2x.
We've been asked to use this graph to estimate the solution to x cubed + 2x is equal to 5x subtract 10.
If we compare the two equations, we can see that we're going to have to draw out the graph of y equals 5x subtract 10.
This will have a gradient of 5 and a y-intercept of negative 10.
We have one point of intersection.
By drawing the line from this point to the x-axis, we can see that x is approximately negative 2.
6.
In this next example, we have been asked to use the graph to estimate the solution to x cubed + 2x is equal to 5x.
Through our comparison, we can see that we're going to need to draw the graph of y is equal to 5x.
This graph will have a gradient of 5 and will go through the origin.
We can see that we have got three points of intersection, the first being here.
If we draw our line up to the x-axis, we can see that the approximate value of x is negative 1.
7.
The next point of intersection is at the origin.
At this point, x has a value of zero.
Our final point of intersection is here.
By drawing our line vertically to the x-axis, we can see that the approximate value of x at this point is 1.
7.
Here are some questions for you to try.
Pause the video to complete your task and resume once you're finished.
Here are the answers.
Your solution might be slightly different, but you always get a bit of leeway with these questions.
For part A, anywhere from negative 1.
5 to negative 1.
1 is fine.
On part B, anywhere from 1.
6 to 2 is fine as well.
Here are some questions for you to try.
Pause the video to complete your task and resume once you're finished.
Here are the answers.
Again, give yourself a little bit of leeway with these solutions.
0.
2 either side of these values will be fine.
That's all for this lesson.
Thanks for watching.
