Graph of the Quadratic Function

The graph of the quadratic function can be rewritten in the form to graph it easily.

Starting from:

1. Vertex coordinates :
2. Equation of the axis :
3. Intersection with the -axis :

Intersection of the Quadratic Function with the -axis and -axis

1. Intersection with the -axis : Find the values of when .
2. Intersection with the -axis : Find the value of when .
   
   
3. Note:
1. The -coordinate of the intersection point with the -axis is called the -intercept, and the coordinate of the intersection point with the -axis is called the -intercept.
2. The graph always intersects the -axis, but it may not intersect the -axis. If it intersects the -axis at two points, those two points are symmetric with respect to the axis.

Sign of , , and in the Graph of the Quadratic Function

1. Sign of : Determines the shape of the graph
1. If the parabola opens upwards,
2. If the parabola opens downwards,
2. Sign of : Determines the position of the axis
1. If the axis is to the left of the -axis, and have the same sign
2. If the axis coincides with the -axis,
3. If the axis is to the right of the -axis, and have opposite signs
3. Sign of : Determines the position of the intersection with the -axis
1. If the intersection with the -axis is above the -axis,
2. If the intersection is at the origin,
3. If the intersection is below the -axis,