### Video Transcript

A curve has the equation π¦ is
equal to π₯ minus three all squared minus four. Find the coordinates of the turning
point of the curve. Circle your answer. Is it three, negative four; three,
four; negative three, four; negative three, negative four; or four, three?

This equation is actually in
completed square form. And there is a formula we can use
to help us find the coordinates of the turning point of the curve. But letβs first consider the
transformation of a curve.

Itβs a transformation of the graph
π of π₯ is equal to π₯ squared. Remember, this is a parabola with a
turning point at the origin, at zero, zero. The graph of π of π₯ minus three
which in this case is π₯ minus three all squared is a translation by the vector
three, zero.

The graph moves three unit in the
positive π₯-direction. Finally, π of π₯ minus three minus
four is in this case π₯ minus three all squared minus four, which weβll notice itβs
the equation of the graph in our question. This time thatβs a translation of
the original by three, negative four. It still moves the original graph
three units to the right, but it also moves it four units down and it takes our
turning point to three, negative four.

And weβve used transformations of
graphs to find the turning point of the equation π₯ minus three all squared minus
four. In fact, a graph with the equation
π₯ plus π all squared plus π has a turning point at negative ππ. This comes from it being a
translation of the graph π¦ is equal to π₯ squared by a vector of negative ππ.

In this case, once again, we can
see that the turning point of the curve is three, negative four.