# Video: Pack 1 β’ Paper 1 β’ Question 11

Pack 1 β’ Paper 1 β’ Question 11

02:55

### Video Transcript

The function π¦ equals π of π₯ has been graphed below. a) Identify the coordinates of the turning point of π¦ equals π of π₯. b) Use the graph to solve π of π₯ equals negative four. And c) use the graph to estimate π of 0.5.

The turning point of a function is in fact the point where it goes from a downward slope to an upward slope. And itβs also the point on a U-shaped parabola. It is the minimum point of our function. But if we actually had an inverted U-shaped parabola, it would be the maximum point of that function, so the maximum point of the graph. So Iβve actually marked on our turning point onto the functional we have here cause itβs on the graph. And the coordinates are negative one, negative five. So therefore, we can say that the turning point of π¦ equals π of π₯ is at the coordinates negative one, negative five. And we can say that because actually we can see that it goes from a downward slope to an upward slope at this point and itβs also the minimum point of our function.

So now, we move on to part b. In part b, we need to use the graph to solve π of π₯ is equal to negative four. So the first thing Iβve actually done is drawn the line π¦ equals negative four because actually thatβs gonna be where our function is gonna be equal to negative four. And we can see that the line π¦ equals negative four actually touches our curve at two points. And if we look up at the π₯-axis, we can see this is where π₯ is equal to negative two or π₯ is equal to zero. So therefore, we can say that the solutions to π of π₯ equals negative four are π₯ equals negative two and π₯ equals zero.

Finally, weβre moving on to part c, use the graph to estimate π of 0.5. So first of all, what does this actually mean? Well, what this means is what is the value of our function when 0.5 is substituted in for π₯. As you can see, Iβve marked on our graph the point where π₯ is equal to 0.5. Iβve then drawn a line down from this point and then across to where it hits the π¦-axis. So therefore, we can see that the value of the function at this point or our π¦-value is equal to negative 2.8. And we know itβs negative 2.8 because there are five little squares in between each unit. So therefore, each one of those can be worth 0.2.

So therefore, weβve solved the problem fully because for part a, we found the coordinates of the turning point of π¦ equals π of π₯ because that was negative one, negative five. For part b, we used the graph to solve π of π₯ equals negative four and that gave us π₯ equals negative two or π₯ equals zero. And for part c, we used the graph to estimate π of 0.5 and it gave us the value negative 2.8.