1. ## Another question

Without graphing explain how you could tell y=a(x-h)^2+k will have no x intercept. Give an example. Please, and thank you.

2. Originally Posted by iorga
Without graphing explain how you could tell y=a(x-h)^2+k will have no x intercept. Give an example. Please, and thank you.
The vertex of this parabola is the point (h, k). Now, either this is the maximum point of the parabola (when a < 0[/tex] or it is the minimum point of the parabola (when a > 0[/tex].

So if, for example, h > 0 and a > 0, then the vertex point is above the x axis, and it is a minimum point which says that all points on the parabola lie above the vertex. So the parabola never crosses the x-axis.

Specific examples:
$y = 3(x - 4)^2 + 2$

$y = -\frac{1}{2}(x + 1)^2 - 3$

-Dan