Download 1 4-3:MODELING WITH QUADRATIC FUNCTIONS Draw the rectangular number next in the series:

A parabola contains points 0,0 , −1,1 and 1,5 .
What is the equation of this parabola in standard
form?
4-3:MODELING WITH
QUADRATIC FUNCTIONS
y  ax 2  bx  c
y  ax 2  bx  c
y  ax 2  bx  c
0  a  0  b 0  c
1  a  1  b  1  c
5  a 1  b 1  c
0c
1 a bc
5  abc
2
2
2
Algebra 2
a  b  c  1

a  b  c  5
a  b  1

a  b  5
a3
b2
y  3x 2  2 x
Draw the rectangular number next in the series:
Find the next two rectangular numbers:
1 2
1 2
23
3 4
45
5 6
5 6
2
3
4
5
6 7
42
1
6
42
1
2
3
4
5
6
# of Dots
Complete the table for the values given
and graph the data:
Total dots
1
2
2
6
3
12
4
20
5
45
# of Dots
# of Dots
Term
Number
3 4
6 7
Term #
Term #
23
30
1) What equation does the
graph suggest?
A Quadratic
(parabola)
78
8 9
56
72
2) Plot the data in your calculator.
Press: STAT>EDIT>L1
Enter the data under Term Number.
3) Use the arrow keys to move through
to L2. Enter the data you found under
Total Dots.
4) Set an appropriate window for the
values.
5) View the graph: Does it resemble
your hand made graph?
The equation is of the form:
y  ax 2  bx  c
a=
b=
c=
1
1
0
Final equation: 2
x x
5) Calculate the equation of the line of
best fit:
Press: STAT>CALC>#5 QuadReg
6) Choose the Lists that your data is
stored under. (Ex. L1, L2) Press:
Enter
1
7)Enter the equation of the line under
2
Y=
x x
8)Graph the equation. Does it fit the
data?
Yes, the parabola graphed goes
through the points.
9) Use your equation to calculate the
100th term in the series.
x 2  x  1002  100  10,100
Homework: p.212 #7-25 odd
2