Graphing the Parabola
Graphing the Parabola 11A
1) 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 . x = -(1) . x = .16
2a 2(-3)
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 ENTER ENTER
The ordered pair will be at the bottom. (-.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: 2nd Graph to find the table
|x |y | |Plot the vertex and roots. Estimate as best you can. |
|-2 |-12 | |Plot the points from the table. | |
|-1 |-2 | |Draw as smooth a curve as possible. |
|0 |2 | |Label with the equation. | |
|1 |0 | | | | | |
|2 |-8 | | | | | |
Do all work on graph paper.
1) y = x2 – 4x + 3 for -1 < x < 5 2) y = -x2 – 2x + 8 for -5 < x < 3
a) Graph – table and y-intercept a) Graph – table and y-intercept
b) Is the vertex a minimum or maximum? b) Is the vertex a min. or max.?
c) Find the axis of symmetry. c) Find the axis of symmetry.
d) Find the vertex. d) Find the vertex.
e) Find the roots. e) Find the roots.
3) y = x2 + 4x + 3 for -5 < x < 1 4) y = -x2 + 2x + 3 for -2 < x < 4
a) Graph – table and y-intercept a) Graph – table and y-intercept
b) Is the vertex a minimum or maximum? b) Is the vertex a min. or max.?
c) Find the axis of symmetry. c) Find the axis of symmetry.
d) Find the vertex. d) Find the vertex.
e) Find the roots. e) Find the roots.
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