Today’s SAT question of the day is an algebra question about the following quadratic equation:

Given that this equation contains the points (-2, 0) and (6, 0), we are asked to find c.

There are multiple ways of solving this, but I will show you the shortest.  The first step is to think about the information we are given: why do they give us these two points?

When factoring (solving a quadratic equation), we usually set it equal to 0 – that is to say, we are setting the y value equal to 0.  The two points they’ve given us have the y value set to 0!  Therefore, these are the solutions to this quadratic equation!

In other words, when we factor x^2 – 4x + c, the solutions we get are -2 and 6.  The factors of c are -2 and 6.  To solve for c, we can just multiply its two factors together to get -12.

You could certainly plug in the x and y values from one of the points and do some arithmetic to solve for c as well, but this is one of those “tutor tricks” that I thought you might like to see.  This medium-difficulty problem is a good opportunity to gain back a few seconds for the harder problems at the end of the section if you can make use of strategies like this one!