[tskalka]

Determine the number of solutions and type of solutions using only the directrix. Find the vertex of the parabola.

F(x)= 4x^2-2x+1

[ebaines]

You can restate the equation for the parabola in the form:

4p(y-y1) = (x-x1)^2

where the vertex of the parabola is at the point (x1,y1), and p is the distance from the vertex to the focus (as well as from the vertex to the directrix). If p is a positive number then the parabola is facing up; if p is negative then the parabola is facing down. So, if the vertex is above the x axis, and p is positive, then the parabola doesn't cross the x axis, and the number of solutions is 0. Same thing of the vertex is below the axis and p is negative. But if the vertex is below the axis and p poistive, or the vertex above the axis and p negative, then the parabola crosses the x axis twice.

Here's a site that shows the directrix and vertex pretty well:

Mathwords: Directrix of a Parabola

[pilliner]

Given that f(x) = 3x + 4/x + 2 and g(x) = 2x - 3.
(a) State the value of x which cannot lie in the domain of F(x).