Lesson video

Hello, my name is Mr Clasper and today we're going to be identifying and interpreting routes, intercepts and turning points of quadratic graphs.

In this lesson, we're going to be identifying and interpreting roots, intercepts and turning points of quadratic graphs.

Here's a graph of y is equal to x squared minus 2x minus eight.

This graph has two roots.

The roots are the two points where the graph intercepts the X axis in this example.

So, our quadratic graph has two roots as it intercepts the X axis at two points.

Some graphs like this one have no roots.

This is because this graph does not intercept the X axis or in other words, there are no values for x that would return a solution of zero for y.

This example has one route or what could be referred to as a repeated route.

So, as you can see, this graph touches the X axis at one point.

So, this graph has one route which is equal to one.

In this example, we're going to identify the turning point.

This is the graph of y is equal to x squared minus 2x minus eight.

The turning point can be found intercepting the line of symmetry of the graph.

Every quadratic graph has a line of symmetry.

So, for this one, our line of symmetry is the line of x is equal to one.

This means that our turning point will happen at the point where x is equal to one and if we substitute x as one into our equation, we'll find that the value of y must be negative nine.

This is the turning point on the graph.

So, the turning point happens at the co-ordinates one, negative nine.

Another name for the turning point is the minimum point.

This is because it represents the smallest possible value for y on the graph.

Another piece of information we can find and identify is the y-intercept.

The y-intercept is the point where the graph will intercept the Y axis.

In our example, this happens here.

The y-intercept is zero, negative eight.

Notice that negative eight is also the constant in our equation.

So, if you have a quadratic equation in this form, the constant will always give you the value for y which is the y-intercept.

Here are some questions 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 question one, the first graph had two solutions as it crosses the X axis at two points.

The second has one solution as it intercepts the X axis at one point and the third has no real solutions as it does not intercept the X axis and for question two, if you make each of the equations equal zero and then solve these, you should find how many solutions each has.

Here's some other questions for you to try.

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

And here are your solutions.

So, remember your roots are the points where your graph will intercept the X axis, your y-intercept is the point where the graph will intercept the Y axis and your turning point is the minimum point of the graph and it's also the point where the line of symmetry would intercept the graph and for question four, the co-ordinate of the y-intercept was zero, negative one.

So, this is because the Y axis is also the line of x equals zero, therefore, the x co-ordinate must be equal to zero.

And here is question five.

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

And here are your solutions.

So again, the roots are the points where our graph meets the X axis, your y-intercept is the point where your graph will meet the Y axis and to write down the equation of the line of symmetry, we can see that the line of symmetry would be x is equal to negative two.

So, if we drew that line, it will be a line of symmetry for our graph.

And here are your last two questions.

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

And here are the solutions.

So, the correct response for question six was the middle graph.

This is because the maximum possible value for y is zero and every other value for y on this graph is less than zero, hence this is a maximum point and for question seven, turning points are below the y-intercept.

Is this true? Always, sometimes never.

The answer is this is sometimes true.

So, for example, if we had a graph similar to the second one from question six positioned in a different way, we could have a turning point, which had a higher value for y than the y-intercept itself.

And that is the end of our lesson.

So, we've been identifying and interpreting routes, intercepts and turning points of quadratic graphs.

Why not try the exit quiz to show off your skills? I'll hopefully see you soon.