Here is the graph of 𝑦 is equal to 𝑓 of 𝑥, where 𝑓 of 𝑥 is a quadratic function. Write down the solutions of 𝑓 of 𝑥 is equal to three.
This might look a little tricky. But let’s just see what’s happened. At the start, we’re told the graph is for the equation 𝑦 is equal to 𝑓 of 𝑥. This just means some function of 𝑥. And in fact, we’re told it’s a quadratic function and we could have spotted that because that graph has the smiley face shape. Then, we’re told to find the solution of 𝑓 of 𝑥 is equal to three.
Notice how the 𝑦 in the first equation has been replaced with three in the second. This means we need to find the solutions of our equation when 𝑦 is equal to three. And we can draw the line 𝑦 is equal to three to help us find these. Remember the line 𝑦 equals three is the horizontal line that passes through the 𝑦-axis at three, as shown.
Notice that the line 𝑦 equals three intersects the curve at two places. The 𝑥-values for these points of intersection will be the solutions to our equation. Let’s add some lines down to our 𝑥-axis from these points. To find the solutions, we need to read the values of 𝑥 from our graph. Before we do though, let’s check the scale.
We can see that five small squares on our 𝑥-axis represent one. We divide by five to work out the value of one small square and that’s one-fifth, which is equal to 0.2. This means the positive solution for 𝑥 is 3.6. It’s three little squares above the number three. And the negative solution for 𝑥 is one little square below the number negative two. So it’s negative 2.2.
The values of 𝑥 when 𝑦 is equal to three and therefore the solutions for 𝑓 of 𝑥 is equal to three are 𝑥 is equal to negative 2.2 and 𝑥 is equal to 3.6.