Graphing the Parabola
1)
11A
a) Graph y = -3x2 + x + 2 for -2 < x < 2
you must set up a table which is explained below
you must also determine the y-intercept which is the point (0, c)
b) Is the vertex a minimum or maximum?
c) Find the axis of symmetry, the vertex, and the roots.
Step 1 - put the equation into the calculator (y = screen)
Step 2 - Make y2 = 0 for the second line (you will need it to find the roots).
Step 3 - Axis of Symmetry: x = -b .
2a
x = -(1) .
2(-3)
x = .16
Step 4 - Vertex or Turning Point:
2nd CALC 1 (for value)
Type in the value for x from the axis of symmetry (.16 ) and hit ENTER
The ordered pair for the vertex will appear on the bottom of the screen. (.16, 2.08)
Min or Max? if a > 0 this has a minimum vertex
if a < 0 this has a maximum vertex
OR....LOOK AT THE PICTURE
Step 5 - ROOTS:
The roots are where the equation or y = 0. (Where it crosses the x-axis).
This is why we put y = 0 into the calculator. The x-axis is where y = 0.
There are usually 2 roots. To find the first:
2nd CALC 5 (for intersect) ENTER
The ordered pair will be at the bottom.
ENTER
ENTER
(-.66, 0)
To find the 2nd root:
2nd CALC 5 (for intersect) DO NOT HIT ENTER!!!!!
You must move the cursor using the blue left and right arrows (not up and
down) closer to the 2nd root.
Once closer: ENTER ENTER ENTER
The ordered pair will be at the bottom. (1,0)
Graph the parabola:
x
y
-2
-12
-1
-2
0
2
1
0
2
-8
2nd Graph to find the table
Plot the vertex and roots. Estimate as best you can.
Plot the points from the table.
Draw as smooth a curve as possible.
Label with the equation.
Do all work on graph paper.
1) y = x2 – 4x + 3 for -1 < x < 5
a) Graph – table and y-intercept
b) Is the vertex a minimum or maximum?
c) Find the axis of symmetry.
d) Find the vertex.
e) Find the roots.
2) y = -x2 – 2x + 8 for -5 < x < 3
a) Graph – table and y-intercept
b) Is the vertex a min. or max.?
c) Find the axis of symmetry.
d) Find the vertex.
e) Find the roots.
3) y = x2 + 4x + 3 for -5 < x < 1
a) Graph – table and y-intercept
b) Is the vertex a minimum or maximum?
c) Find the axis of symmetry.
d) Find the vertex.
e) Find the roots.
4) y = -x2 + 2x + 3 for -2 < x < 4
a) Graph – table and y-intercept
b) Is the vertex a min. or max.?
c) Find the axis of symmetry.
d) Find the vertex.
e) Find the roots.