Graphing the Parabola
a) Graph y = x2 – 4x + 3 for -1 < x < 5
b) Is the vertex a minimum or maximum?
c) Find the axis of symmetry, the vertex, and the roots.
1)
The first thing you should do is put the equation into the calculator.
While you are in the y= screen, you might as well put in y = 0 for the second line (you will need it to find
the roots).
Min or Max?
LOOK AT THE PICTURE
Axis of Symmetry:
x = -b . x = -(-4). x = 4 .
[a is the coefficient of x2 (1) and b is the coef. of x (-4)]
2a
2(1)
2
a = 1 b = -4
x=2
Finding the vertex:
2nd CALC 1 (for value)
Type in the value for x (x= 2) and hit ENTER
The ordered pair for the vertex will appear on the bottom of the screen. (2,-1)
Finding the 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 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.
1st Root: _________
To find the 2nd root:
2 CALC 5 (for intersect) DO NOT HIT ENTER!!!!!
You must move the cursor using the blue left and right arrows (not up and down) close to the 2nd root.
Once close: ENTER ENTER ENTER The ordered pair will be at the bottom. (1,0)
2nd root:
.
nd
Fill out the table, plot the points, draw a smooth curve, and label. (use graph on back).
x
-1
0
1
2
3
4
5
y
2) a) Graph: y = 2x2 +3x – 5
b) Is the vertex a minimum or maximum?
c) Find the axis of symmetry.
d) Find the vertex.
e) Find the roots.
3) a) Graph: y = -x2 + 5x + 2
b) Is the vertex a min. or max.?
c) Find the axis of symmetry.
d) Find the vertex.
e) Find the roots.
Graphing the Parabola
when the numbers aren’t so nice
2
1)
a) Graph y = -3x + x + 2
b) Is the vertex a minimum or maximum?
c) Find the axis of symmetry, the vertex, and the roots.
The first thing you should do is put the equation into the calculator. While you are in the y= screen, you
might as well put in y = 0 for the second line (you will need it to find the roots).
Min or Max?
LOOK AT THE PICTURE
Axis of Symmetry:
x = -b .
x = -(1) .
2a
2(-3)
[a is the coefficient of x2 (-3)and b is the coef. of x (1)]
x = .16
Finding the vertex: If the axis of symm. is an integer, then you can find the ordered
pair for the vertex in the table. If not, we will use the calculator.
2nd CALC 1 (for value)
Type in the value for x (.16 ) and hit ENTER
The ordered pair for the vertex will appear on the bottom of the screen. (.16, 5.08)
Finding the 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 y = 0.
There are usually 2 roots. To find the first:
2 CALC 5 (for intersect) ENTER ENTER ENTER
The ordered pair will be at the bottom.
(1.47, 0)
nd
To find the 2nd root:
2 CALC 5 (for intersect) DO NOT HIT ENTER!!!!!
You must move the cursor using the blue left and right arrows (not up and down) close to the 2nd root.
Once close: ENTER ENTER ENTER The ordered pair will be at the bottom. (-1.14,0)
nd
Graph the parabola:
x
y
-2
-1
0
1
2
-9
1
5
3
-5
-Plot the vertex. Estimate as best you
can.
-Plot the points from the
table.
-Draw as smooth a curve as possible.
-Label with the equation.
1) a) Graph: y = -3x2 + x + 2
b) Is the vertex a minimum or maximum?
c) Find the axis of symmetry.
d) Find the vertex.
e) Find the roots.
2) a) Graph: y = x2 – 3x – 4
b) Is the vertex a min. or max.?
c) Find the axis of symmetry.
d) Find the vertex.
e) Find the roots.
3) a) Graph: y = 2x2 + x - 3
b) Is the vertex a minimum or maximum?
c) Find the axis of symmetry.
d) Find the vertex.
e) Find the roots.
4) a) Graph: y = - x2 – 4x + 3
b) Is the vertex a min. or max.?
c) Find the axis of symmetry.
d) Find the vertex.
e) Find the roots.