Lesson video

Hello, my name is Mr. Clasper, and today we are going to be solving quadratic equations graphically.

In this lesson, we're going to look at how to solve a quadratic equation graphically.

So this means we're going to find solutions purely by using the graph.

So this is an example of the equation, y is equal to x squared plus five x minus three.

How could we use the graph to solve x squared plus five x minus three is equal to zero? If we're going to solve x squared plus five x minus three is equal to zero, this must mean that the value of y is zero, or in other words, y equals zero.

The line y equals zero is the X-axis.

As every coordinate on the X-axis has a y coordinate of zero.

Therefore, our solutions can be found at the points where our graph intersects the X-axis.

And it does so here, and also here.

This means our equation has two solutions.

One of our solutions is that x is equal to 0.

55, so when x is equal to 0.

55, the value of y is zero, and when x is equal to negative 5.

55.

So if we substitute x is equal to negative 5.

55 into our equation, we will also return a value of zero.

How can we use the graph to solve x squared plus five x minus three is equal to five? Well, in this case, we would assume that the value of y must be equal to five.

So I'm looking for the point or points on my graph, where the value of y is equal to five.

To do this, I could draw the line of y equals five.

So all of the coordinates on this line have a y value of five.

And again, I'm looking for the two points where my graph intersects this line.

This would happen here, which would give us a value of x is equal to 1.

28.

And it also happens here, which it gives a value of negative 6.

28.

Here's a question for you to try.

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

And here are your solutions.

So for part A, we need to find a point where the equation is equal to zero.

So these are the roots of our equation, which would be approximately 0.

3 and negative 3.

3.

If you've got values which are close to these, that should be fine as they are estimates to solutions.

And for part B, we need to find a point where the graph is equal to four.

So we're finding the point where the graph intersects the line y is equal to four.

And again, this happens twice at the points where x is approximately 1.

2 and where x is approximately negative 4.

2.

Here's another question for you to try.

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

And here are your solutions.

So on our graph we can see that we have two routes at x is equal to 0.

5 and x is equal to negative one.

These are our two solutions.

To check this, if we substitute both 0.

5 and negative one into the given equation, we should find a y value of zero.

Here's question three.

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

And here is the solution.

So for part A, we need to find a point where the graph is equal to zero.

This would be our two routes.

So our approximate solutions could be 0.

5 and negative 7.

1.

Again, as these are approximate, if you have two solutions which are close to these, they should be fine.

And here is part B.

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

This time we're going to estimate when the graph is equal to negative one, so we're going to draw or think of the line of y is equal to negative one, and where this point crosses our graph it should give us approximate solutions of 0.

9 and negative 7.

6.

Here's part C.

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

And here is the solution.

So the question asked why we can't find a solution to one minus two x minus 0.

3 x squared is equal to six.

Well the reason for this is that our graph never reaches a y value of six.

So if we look at our graph, our maximum point is approximately where y is equal to 4.

4.

Therefore, we don't have any solutions at this point.

And here is part D.

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

And here is your solution.

So the question was, how do we use the graph to solve 0.

3 x squared plus two x is equal to one.

The answer is exactly the same as your answer to part A as the only thing we have done is rearrange the equation.

So we've taken the graph and we've rearranged this equation into a different form.

However, the solutions will still be the same.

And that is the end of our lesson.

So we've been solving quadratic equations graphically, why not give the exit quiz a go to sharpen up your skills? I'll hopefully see you soon.