# Dimension and Graph

Topics: Dimension, Plus and minus signs, Quadratic equation Pages: 2 (714 words) Published: December 7, 2012
Locus of Parabola

going through an equation......

while b is varied and the variables a and c are held constant. So let's start with the graph where all variables, a, b and c, are equal to 1.

The graph opens upward because a is postive. If a was negative the graph would open in the negative direcction. It is not symmetrical around the y-axis because c = 1. Because c = 1, when x = 0, the parabola passes through the point (0, 1). If c equaled 0, then the parabola would be symmetrical around the y-axis.

Now let's look at what happens when we change b, while a and c remain 1.

For these positive values of b, the graph always intersects the y-axis at the point (0, 1). The vertex is always to the left of the graph when b > 0. When b = 0, the vertex is on the y-axis. We know that where the parabola intersects or hits the x-axis is where the real roots of that particular equation occur. For those graphs that do not intersect or hit the x-axis, then they do not have any real roots. For example, when b = 1, the graph does not hit the x-axis, therefore it does not have any real roots. Notice that when tb is positive, the real roots occur on the negative side of the y-axis.

Now let's see what happens when b is negative.

For these negative values of b, the graph always intersects the y-axis at the point (0, 1). The vertex is always to the right of the graph when b > 0. When b = 0, the vertex is on the y-axis. We know that where the parabola intersects or hits the x-axis is where the real roots of that particular equation occur. For those graphs that do not intersect or hit the x-axis, then they do not have any real roots. For example, when b = -1, the...