1. Sept 3rd
Learning outcome: To discover what happens
to a parabola’s graph when you change the
numbers in the equation?
 Launch:
 1. Graph your table from last week’s
pattern
 2. Do you recall what this type of graph is
called?
x 0 1 2 3 4 n
y 0 1 4 9 16 n2

2. Explore: Parabola Lab
1.What happens to a parabola’s graph when
you change the numbers in the equation?
 a. On graph paper, graph y = (x-2)(x-2).
Labeling important points including the vertex
(lowest point) and line of symmetry (line that
cuts the graph in half).
 b. Use your graphing calculator to find the
equations of 2 parabolas with different graphs
that also open upward and still have a vertex
at (2, 0). Use 2 different colored pencils to
add the sketches along with the equations to
the graph from #1.

3. Explore: Parabola Lab
 c. Use your calculator to find the equation of 2
different parabolas that open downward, each
with its vertex on the x-axis at x = 2. Use 2 different
colored pencils to add the sketches along with
the equations to the graph from #1 a and b.
 d. Use your calcuator to find the equation of a
parabola that opens downward with a vertex of
(-4, 0). What is the equation of your parabola’s
line of symmetry?
 e. Choose a new point on the x-axis and find at
least 3 equations of parabolas that touch the x-
axis only at that one point.

4. Explore: Parabola Lab part 2
 2. Use your graph y = x2 from the launch to do the
following:
 a. Find a way to stretch y = x2 vertically (make it
narrower), but the vertex stays in the same place.
Use a colored pencils to add the sketch along
with the equations to the graph from the launch.
 b. Find a way to compress y = x2 vertically (make it
flatter), but the vertex stays in the same place. Use
a colored pencils to add the sketch along with the
equations to the graph from the launch.
 c. Find a way to open y = x2 downward, but the
vertex stays in the same place and is the same
shape as y = x2. Use a colored pencils to add the
sketch along with the equations to the graph from
2a.

5. Explore: Parabola Lab part 2
 2d. Find a way to move y = x2 5 units down
(but remain the same shape and size and
vertex at (0,5)). Use a colored pencils to add
the sketch along with the equations to the
graph from the launch.
 2e. Find a way to move y = x2 3 units to the
right (but remain the same shape and size
and vertex at (3,0)). Use a colored pencils to
add the sketch along with the equations to
the graph from the launch.
 2f. Find a way to move y = x2 3 units left and
stretch vertically Use a colored pencils to add
the sketch along with the equations to the
graph from the launch.

6. Parabola Lab challenge
 3. Find a way to change the equation y =
x 2 parabola vertically compressed, open
down, move six units up and move two
unites to the left. Where is the vertex of
your new parabola?

7. Summary
 Now that you are a parabola expert can
you write a general equation for a
parabola that can be stretched or shifted
any direction?