### 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 itβs 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 Iβve actually marked on our
turning point onto the functional we have here cause itβs 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 itβs 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 Iβve actually
done is drawn the line π¦ equals negative four because actually thatβs 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, weβre 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, Iβve marked on our
graph the point where π₯ is equal to 0.5. Iβve 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 itβs 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, weβve 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.