423-432_SB_AG1_SE_U05_A29.indd Page 423 18/05/13 4:01 PM user-g-w-728
/Data%20Disk/Anuj/18-05-2013
Introduction to Quadratic Functions
ACTIVITY 29
Touchlines
Lesson 29-1 Modeling with a Quadratic Function
My Notes
Learning Targets:
• Model a real-world situation with a quadratic function.
• Identify quadratic functions.
• Write a quadratic function in standard form.
SUGGESTED LEARNING STRATEGIES: Create Representations,
Interactive Word Wall, Marking the Text, Look for a Pattern, Discussion
Groups
Coach Wentworth coaches girls’ soccer and teaches algebra. Soccer season is
starting, and she needs to mark the field by chalking the touchlines and goal
lines for the soccer field. Coach Wentworth can mark 320 yards for the total
length of all the touchlines and goal lines combined. She would like to mark
the field with the largest possible area.
© 2014 College Board. All rights reserved.
Goal
Goal line
Goal
Goal line
Touchline
Touchline
FIFA regulations require that all soccer fields be rectangular in shape.
1. How is the perimeter of a rectangle determined? How is the area of a
rectangle determined?
CONNECT TO SPORTS
FIFA stands for Fédération
Internationale de Football
Association (International
Federation of Association
Football) and is the international
governing body of soccer.
Activity 29 • Introduction to Quadratic Functions
423
423-432_SB_AG1_SE_U05_A29.indd Page 424 7/29/13 9:13 PM deepaksharma 000
/103/SB00001_DEL/work/indd/SE/M01_Middile_School/Algebra_01/Application_files/SE_ ...
Lesson 29-1
Modeling with a Quadratic Function
ACTIVITY 29
continued
My Notes
2. Complete the table below for rectangles with the given side lengths. The
first row has been completed for you.
Length
(yards)
Width
(yards)
Perimeter
(yards)
Area (square yards)
10
150
320
1500
20
320
40
320
60
320
80
320
100
320
120
320
140
320
150
320
l
320
4. Is a 70-yd by 90-yd rectangle the same as a 90-yd by 70-yd rectangle?
Explain your reasoning.
5. Graph the data from the table in Item 2 as ordered pairs.
Area of Rectangle (yd2)
7000
6000
5000
4000
3000
2000
1000
20 40 60 80 100 120 140 160
Length of Rectangle (yd)
424
SpringBoard® Mathematics Algebra 1, Unit 5 • Quadratic Functions
© 2014 College Board. All rights reserved.
3. Express regularity in repeated reasoning. Describe any
patterns you observe in the table above.
423-432_SB_AG1_SE_U05_A29.indd Page 425 24/03/14 9:19 AM user-g-w-728
Unsaved...
Lesson 29-1
Modeling with a Quadratic Function
ACTIVITY 29
continued
6. Use the table and the graph to explain why the data in Items 2 and 5 are
not linear.
My Notes
7. Describe any patterns you see in the graph above.
8. What appears to be the largest area from the data in Items 2 and 5?
(80,6400)
l and w: 80
area: 6400
© 2014 College Board. All rights reserved.
9. Write a function A(l) that represents the area of a rectangle whose
length is l and whose perimeter is 320.
The function A(l) is called a quadratic function because the greatest degree
of any term is 2 (an x2 term). The standard form of a quadratic function is
y = ax2 + bx + c or f(x) = ax2 + bx + c, where a, b, and c are real numbers
and a ≠ 0.
10. Write the function A(l) in standard form. What are the values of a, b,
and c?
Activity 29 • Introduction to Quadratic Functions
425
423-432_SB_AG1_SE_U05_A29.indd Page 426 7/29/13 9:14 PM deepaksharma 000
/103/SB00001_DEL/work/indd/SE/M01_Middile_School/Algebra_01/Application_files/SE_ ...
Lesson 29-1
Modeling with a Quadratic Function
ACTIVITY 29
continued
My Notes
Check Your Understanding
11. For the function f(x) = x2 + 2x + 3, create a table of values for
x = −3, −2, −1, 0, 1. Then sketch a graph of the quadratic function
on grid paper.
12. Barry needs to find the area of a rectangular room with a width that is
2 feet longer than the length. Write an expression for the area of the
rectangle in terms of the length.
13. Critique the reasoning of others. Sally states that the equation
g(x) = x3 + 10x2 − 3x represents a quadratic function. Explain why
Sally is incorrect.
14. Write the quadratic function f(x) = (3 − x)2 in standard form.
LESSON 29-1 PRACTICE
15. Create tables to graph y = 3x and y = 3x2 on grid paper. Explain the
differences between the graphs.
16. Pierre uses the function r(t) = t + 2 to model his rate r in mi/h
t minutes after leaving school. Complete the table and use the data
points to graph the function.
t
r(t)
0
1
3
4
17. Pierre uses the function d(t) = t(t + 2) to model his distance d in miles
from home. Add another column to your table in Item 16 to represent
d(t). Sketch a graph of d(t) on the same coordinate plane as the graph
of r(t).
18. What types of functions are represented in Items 16 and 17?
19. Write each quadratic function in standard form.
a. g(x) = x(x − 2) + 4
b. f(t) = 3 − 2t2 + t
20. Attend to precision. Determine whether each function is a quadratic
function. Justify your responses.
2
b. f (a) = a + 4a − 3
a. S(r) = 2πr2 + 20πr
2
c. f(x) = 4x2 − 3x + 2
d. g(x) = 3x−2 + 2x − 1
f. h(x) = 42 − 3x + 2
e. f(x) = 42x − 3
x
426
SpringBoard® Mathematics Algebra 1, Unit 5 • Quadratic Functions
© 2014 College Board. All rights reserved.
2