Transcript 7.2 Write Quadratic Functions and Models

7.2
Write Quadratic Functions
and Models
7.2 HW Quiz: Sept. 15 (Wednesday)
7.1-7.2 Quiz: Sept. 17 (Friday)
7.1,7.2,7.7 Test: Sept. 22 (Wednesday)
Vocabulary
 Quadratic
Regression: the
process of finding the best-fitting
quadratic model for a set of data
 Curve
Fitting: find a line or curve
that matches a set of data points
Quadratic Regression

The table shows the population of a bacteria
culture from day 5 to day 30. Use a graphing
calculator to find the best-fitting quadratic model.
(quadratic regression)
Day
Population
5
10
15
20
25
30
60
135
240
370
500
740
Quadratic Regression
Standard
Form
y = 0.66x2 + 3.3x + 32.5
You Try:

Use a graphing calculator to find the bestfitting quadratic model for the given values:
(4, 56), (8, 100), (12, 165), (16, 255), (20, 360), (24, 500)
y = 0.714x2 + 2.071x + 37
Transformations
•
a = vertical shrink / stretch by a
•
(h, k) = vertex of parabola
•
(x, y) = point on parabola
(there are infinitely many!!)
•
p , q = x-intercepts of parabola
You Need to know these forms for
Quadratic Functions:

Vertex Form: (h, k) represent the vertex
y = a(x – h)2 + k

Intercept Form: p and q represent intercepts
on the x-axis
y = a(x – p)(x – q)

Standard Form:
y = ax2 + bx + c
+2
-3
0
5
0+2
2
y = 2(x + 2)2 – 3
5
-3
3
2
y  ( x  2)  1
4
+3
-4
-2
-2 + 3
1
y = 1(x + 3)(x – 2)
-2 – 2
y  3( x  4)( x  2)
Homework – Start NOW!

P. 257 #1-10, #17-20