Consider the locus of the vertices of the set of parabolas graphed from
Show that the locus is the parabola
In this graph, the values of b range from Ð3 to 3.
The parabolas all intercept at the point (0,1).
Using the graphing calculator, it is clear that the vertices of the parabolas graphed above are
(Ð1.5, -1.25), ( -1, 0), ( -.5, .75), (0, 1), ( .5, .75), ( 1, 0),
Using slope and y-intercept form, the equations of the lines that go through points (1, 0), ( -1, 0), and (0, 1) are
The graph below shows that the product of the equations of the two lines is a parabola. The vertices of each parabola with the equation
maps to the graph below.
To view a GSP file of this parabola click here.