# Video: AQA GCSE Mathematics Higher Tier Pack 5 β’ Paper 2 β’ Question 23

Here is the graph of π¦ = π(π₯), where π(π₯) is a quadratic function. Write down the solutions of π(π₯) = 3.

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### Video Transcript

Here is the graph of π¦ is equal to π of π₯, where π of π₯ is a quadratic function. Write down the solutions of π of π₯ is equal to three.

This might look a little tricky. But letβs just see whatβs happened. At the start, weβre told the graph is for the equation π¦ is equal to π of π₯. This just means some function of π₯. And in fact, weβre told itβs a quadratic function and we could have spotted that because that graph has the smiley face shape. Then, weβre told to find the solution of π of π₯ is equal to three.

Notice how the π¦ in the first equation has been replaced with three in the second. This means we need to find the solutions of our equation when π¦ is equal to three. And we can draw the line π¦ is equal to three to help us find these. Remember the line π¦ equals three is the horizontal line that passes through the π¦-axis at three, as shown.

Notice that the line π¦ equals three intersects the curve at two places. The π₯-values for these points of intersection will be the solutions to our equation. Letβs add some lines down to our π₯-axis from these points. To find the solutions, we need to read the values of π₯ from our graph. Before we do though, letβs check the scale.

We can see that five small squares on our π₯-axis represent one. We divide by five to work out the value of one small square and thatβs one-fifth, which is equal to 0.2. This means the positive solution for π₯ is 3.6. Itβs three little squares above the number three. And the negative solution for π₯ is one little square below the number negative two. So itβs negative 2.2.

The values of π₯ when π¦ is equal to three and therefore the solutions for π of π₯ is equal to three are π₯ is equal to negative 2.2 and π₯ is equal to 3.6.