Posted by tc on Thursday, January 26, 2012 at 11:01pm.
A parabola which opens up has a lowest point and a parabola which opens down has a highest point.
The highest or lowest point on a parabola is called the vertex.
This point, where the parabola changes direction, is called the "vertex".
To determine the vertex of the graph of a quadratic function:
f(x) = a x ^ 2+ b x + c
we can either:
1) Use the method of completing the square to rewrite the function in the form:
f(x) = a ( x - h ) ^ 2 + k
The vertex poit is a point with coordinates: (h, k)
x coordinates of the vertex = h
y coordinates of the vertex = k
OR
2) Use the formula:
x coordinates of the vertex = - b / 2a
y coordinates of the vertex = f ( x ) = c - b ^ 2 / 4a
The axis of symmetry is a vertical line through the vertex.
The equation of the axis of symmetry is the equation of the vertical line passing through x and y coordinate of the vertex:
The equation of the axis of symmetry:
x = x coordinate of the vertex
For each value of y
x = - b / 2a
y coordinates of the vertex = f ( x ) = f ( x = - b / 2a ) = c - b ^ 2 / 4a