Solve x^2 - 6x + 8 < 0

To see the answer more clearly, we can sketch the function. First, we start by sketching the parabola (curve). If we have a positive x^2 term then we have a U shaped parabola and if it is negative, i.e. -x^2, we have an n shaped parabola. Here, our x^2 term is positive so we will draw a U shaped curve -> Don't draw the axes on yet!The question is asking us to solve for one or two values of x. The x^2 - 6x + 8 equation is often written as equal to y. This is called a Quadratic Equation. ( x^2 - 6x + 8 = y). Our next step is to set this quadratic equation to 0 (i.e. y=0). We then factorise the equation giving (x - 2)(x - 4) = 0. This gives us solutions of x = 2 and x = 4. We have solved for the x values where y = 0 . Graphically, that is on our graph, we have found the x-intercepts/where the curve crosses the x axis. We can now draw our x axis on our graph -> a straight horizontal line that cuts the curve in two places (two because that is the number of x solutions we have found, x=2 and x=4). As both of these solutions are positive, our y axis lies to the left of our curve. Now we look at the question again. It is asking us for all solutions of x that make x^2 - 6x + 8 LESS THAN zero. This is equivalent to asking where y is less than zero. Where on the graph is y < 0? Below the x axis. Therefore, we must find any points on the curve that lie below the x axis. We see that this occurs when 2 < x < 4. This is our solution.