Assignment 3

Quadratic Equations

Investigation 1.

Consider the locus of the vertices of the set of parabolas graphed from

**Show that the locus is the
parabola **

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**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), **

**(1.5, -1.25).**

** **

**Using slope and
y-intercept form, the equations of the lines that go through points (1, 0), (
-1, 0), and (0, 1) are**

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**and **

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**Interestingly, **

**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. **

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**To view a GSP file of this
parabola click **here**.**

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