I'm working on solving inequalities for an assignment. The instructions also request that I draw a 'sign chart' along with each solution. I've never heard of a 'sign chart' before, and the internet also seems to have a limited amount of information. From what I can gather...
PurpleMath never actually refers to these diagrams as sign charts either, but I assume these 'factor charts' are synonymous.
The first image is a sign chart for (x + 4)(x – 2)(x – 7) > 0. I know that this has roots at -4, 2, and 7. These are indicated in between columns. The factors are written along rows. The -/+ is determined by evaluating a test point in a range dependent on the columns in each factor. (This is just my understanding - I could by all means be very, very incorrect.) For example - cell "B3" - the range is -4 < TEST < 2. 0 is in this range, so I will evaluate (x-2) for 0. The resulting sign is -, so I mark that in cell B3. I evaluate all other cells in that column, except for the top. The top cell of each column is determined by the resulting sign of all signs below it (in column 3, - * - = +).
However, my intuition fails me when the problems become more complex. Take, for example, 4x^2 + 8x < 6. When solved using the quadratic equation, x equals a messy (-2 +/- sqrt(10) ). I don't understand what to put along the columns and rows. What goes where?