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Hi, I'm Miss Davies.

In this lesson, we're going to be finding approximate solutions for quadratic graphs.

Sometimes we are given a quadratic graph but asked to solve a different equation.

Here is the graph of y is equal to five x squared subtract three x subtract one.

It is possible to solve the equation five x squared subtract four x is equal to zero from this graph.

Five x squared subtract four x can be manipulated to become five x squared subtract three x subtract one by adding x and subtracting one.

Five x squared subtract four x is equal to zero would then become five x squared subtract three x subtract one is equal to x subtract one.

By plotting the graph, y is equal to x subtract one onto the graph of y is equal to five x squared subtract three x subtract one, we can find the solutions to five x squared subtract four x is equal to zero.

We can see from our graph that we have got two points of intersection at x is equal to zero and x is equal to 0.

8.

By substituting in x is equal to zero and x is equal to 0.

8 into this equation, will verify the solutions.

Five multiplied by zero squared subtract four multiplied by zero is zero.

So zero is a solution.

Five multiplied by 0.

8 squared subtract four multiplied by 0.

8 is also zero.

This means that x is equal to 0.

8 is a solution to the equation.

Here is the graph of y is equal to five x squared subtract the three x subtract one.

By sketching a suitable graph, we are going to approximate the solutions to the equation five x squared subtract five x add one is equal to zero.

To go from negative five x to negative three x, we're going to add two x to both sides of this equation.

Then we need negative one.

To go from positive one to negative one, we're going to subtract two from both sides of the equation.

We can then plot the graph of y is equal to two x subtract two.

We can see that this has two points of intersection with our quadratic graph.

The x-coordinates of these two points are approximately 0.

15 and 0.

75.

These are the approximate solutions to the equation five x squared subtract five x add one is equal to zero.

Here is a question for you to try.

Pause the video to complete your task and resume once you're finished.

Here is the answer.

The linear graph that should have been drawn is y is equal to x add one.

Here is a question for you to try.

Pause the video to complete your task and then resume once you're finished.

Here is the answer.

The linear graph that you should have drawn on today's grid is y is equal to negative x subtract two.

Here is a question for you to try.

Pause the video to complete your task and resume once you're finished.

Here is the answer.

To find approximate solutions to this equation, you should have drawn the linear graph of y is equal to negative x subtract two.

That's all for this lesson.

Thanks for watching.