Mathematical Investigations III
Name:
Mathematical Investigations III - A View of the World
Quadratic Vertices
We want to consider the general quadratic function, ƒ(x) = ax2 + bx + c, and what happens to the
graph of the function as the parameters a, b, and c change. Specifically, let's look at each parameter
in turn and how it affects the position of the vertex of the parabola. You will explore these options by
using the Mathematica notebook "QuadraticVertices.nb."
Step 1: Open the notebook and use each of the sliders. If possible, make some conjectures about how
each of the parameters a, b, and c affect the vertices of the quadratics.
Now we'll look at each parameter one at a time.
Step 2: Consider the quadratic function y  x 2  4x  C .
a. Use complete sentences to describe what appears to be happening to the parabola as you move the
slider to vary C.
b. Choose one specific value of C and find the resulting vertex. Be sure that your table mates all
choose a different C value. Compare the location of your vertices.
c. State the equation of the "locus" of vertices of the function y  x 2  4x  C as C varies.
Poly 2.1
Rev. S11
Mathematical Investigations III
Name:
Step 3: Consider the quadratic function y  x 2  Bx  6 .
a. Use complete sentences to describe what appears to be happening to the parabola as you move the
slider to vary B.
b.
For two or more specific values of B, find the vertex of each resulting parabola. Again, be sure
that your table mates are choosing different values of B. Now look at all (yours and theirs) of the
coordinates for the vertices. What do you notice?
c.
Find the equation of the "locus" of vertices of the function y  x 2  Bx  6 as B varies.
Poly 2.2
Rev. S11
Mathematical Investigations III
Name:
Step 4: Consider the quadratic function y  Ax 2  4x  6 .
a. Use complete sentences to describe what appears to be happening to the parabola as you move the
slider to vary A.
b.
For two or more specific values of A, find the vertex of each resulting parabola. Yet again, be
sure that your table mates are choosing different values of A. Now look at all (yours and theirs)
of the coordinates for the vertices. What do you notice?
c.
Find the equation of the "locus" of vertices of the function y  Ax 2  4x  6 as A varies.
Poly 2.3
Rev. S11