### Video Transcript

The graph shows the function π of
π₯ equals two π₯ squared minus four π₯ minus six. What is the solution set of π of
π₯ equals zero? What is the solution set of π of
π₯ equals negative six?

The solution set for π of π₯
equals zero will be the places where two π₯ squared minus four π₯ minus six equals
zero. And on the graph, thatβs the place
where they cross the π₯-axis. The π¦ equals zero across the
π₯-axis. In this case, we have a solution at
negative one and at positive three. So for π of π₯ equal to zero, the
solution set is negative one, three. Remember, this is not a
coordinate. These are the π₯-values for which
π of π₯ equals zero. And weβve given them in set
notation.

The π₯-axis, as weβve said, is the
place where π¦ equals zero. The line π of π₯ equals zero is
the π₯-axis. But what would we do if we were
using a graph to look at π of π₯ equals negative six? This would be the place or the
places where our quadratic cross the line π¦ equals negative six. And in this graph, we see thatβs
happening twice. It happens when π₯ equals zero and
when π₯ equals two. In set notation, weβre saying the
two π₯-values for which π of π₯ equals negative six are zero and two.