Video: Pack 1 β€’ Paper 1 β€’ Question 11

Pack 1 β€’ Paper 1 β€’ Question 11

02:55

Video Transcript

The function 𝑦 equals 𝑓 of π‘₯ has been graphed below. a) Identify the coordinates of the turning point of 𝑦 equals 𝑓 of π‘₯. b) Use the graph to solve 𝑓 of π‘₯ equals negative four. And c) use the graph to estimate 𝑓 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 it’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 I’ve actually marked on our turning point onto the functional we have here cause it’s on the graph. And the coordinates are negative one, negative five. So therefore, we can say that the turning point of 𝑦 equals 𝑓 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 it’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 𝑓 of π‘₯ is equal to negative four. So the first thing I’ve actually done is drawn the line 𝑦 equals negative four because actually that’s gonna be where our function is gonna be equal to negative four. And we can see that the line 𝑦 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 𝑓 of π‘₯ equals negative four are π‘₯ equals negative two and π‘₯ equals zero.

Finally, we’re moving on to part c, use the graph to estimate 𝑓 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, I’ve marked on our graph the point where π‘₯ is equal to 0.5. I’ve then drawn a line down from this point and then across to where it hits the 𝑦-axis. So therefore, we can see that the value of the function at this point or our 𝑦-value is equal to negative 2.8. And we know it’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, we’ve solved the problem fully because for part a, we found the coordinates of the turning point of 𝑦 equals 𝑓 of π‘₯ because that was negative one, negative five. For part b, we used the graph to solve 𝑓 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 𝑓 of 0.5 and it gave us the value negative 2.8.

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