### (8) Lesson 4.8

1. Determine whether each table represents a linear or nonlinear function. Explain. 1. 2. 3. 4. Course 3, Lesson 4-8
2. Course 3, Lesson 4-8 ANSWERS 1. nonlinear; the rate of change is not constant. 2. nonlinear; the rate of change is not constant. 3. nonlinear; the rate of change is not constant. 4. linear; the rate of change is 1 2
3. HOW can we model relationships between quantities? Functions Course 3, Lesson 4-8 .
4. Course 3, Lesson 4-8 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Functions • 8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line. • 8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph. Sketch a graph that exhibits the qualitative features of a function that has been described verbally. Mathematical Practices 1 Make sense of problems and persevere in solving them. 3 Construct viable arguments and critique the reasoning of others. 4 Model with mathematics. 7 Look for and make use of structure.
5. To • graph a quadratic function, • use the graph to estimate a value Course 3, Lesson 4-8 Functions
6. • quadratic function Course 3, Lesson 4-8 Functions
7. 1 Need Another Example? 2 3 Step-by-Step Example 1. Graph y = x2. To graph a quadratic function, make a table of values, plot the ordered pairs, and connect the points with a smooth curve.
8. Answer Need Another Example? Graph y = 5x2.
9. 1 Need Another Example? 2 Step-by-Step Example 2. Graph y = –x2 + 4.
10. Answer Need Another Example? Graph y = –x2 – 2.
11. 1 Need Another Example? 2 3 4 Step-by-Step Example 3. The function d = 4t2 represents the distance d in feet that a race car will travel over t seconds with a constant acceleration of 8 feet per second. Graph the function. Then use the graph to find how much time it will take for the race car to travel 200 feet. Time cannot be negative, so only use positive values of t. Locate 200 on the vertical axis. Move over to the graph and locate the corresponding value for the time. The car will travel 200 feet after about 7 seconds.
12. Answer Need Another Example? The function d = 16t2 represents the distance d in feet that a skydiver falls in t seconds. Graph the equation. Then use the graph to find how much time it will take for the skydiver to fall 400 feet. 5 s;
13. 1 Need Another Example? 2 3 Step-by-Step Example 4. The function h = 0.66d 2 represents the distance d in miles you can see from a height of h feet. Graph this function. Then use the graph to estimate how far you could see from a hot air balloon 1,000 feet in the air. Distance cannot be negative, so use only positive values of d. At a height of 1,000 feet, you could see approximately 39 miles.
14. Answer Need Another Example? The equation d = 16.065t2 describes the distance d in feet that a stone falls off a cliff during time t. Graph this function. Then use the graph to estimate how long it would take a stone to fall 200 feet. about 3.5 s;
15. How did what you learned today help you answer the HOW can we model relationships between quantities? Course 3, Lesson 4-8 Functions
16. How did what you learned today help you answer the HOW can we model relationships between quantities? Course 3, Lesson 4-8 Functions Sample answers: • One type of nonlinear relationship is a quadratic function. The graph of a quadratic function is a parabola. • The equation y = ax2 + bx + c represents a quadratic function.
17. Explain the steps you would use to graph a quadratic function. Ratios and Proportional RelationshipsFunctions Course 3, Lesson 4-8