Chapter 5.8 Radical Equations & Inequalities Standard & Honors Algebra II Mr. Gilbert Chapter 5.8 Radical Equations & Inequalities Standard & Honors 9/21/2018

Agenda Warm-up (next slide) Return Class work Lesson Homework Check your answers Return Class work Lesson Homework 9/21/2018

Class Work: Warm-up 7.9 (5 min.) Solve: 2h4 – h3 +h2 +h – 3 h2-1 Find the third term of (x+y)34 9/21/2018

Class Work: Warm-up 7.9 (5 min.) Solve: 2h4 – h3 +h2 +h – 3 h2-1 = 2h2 –h +3 Find the third term of (x+y)34 = 561 x32y2 9/21/2018

7.9 Square Root Functions and Inequalities Example 1 Graph a Square Root Function (4) Example 2 Solve a Square Root Problem (4) Example 3 Graph a Square Root Inequality (7) You will need a graphing calculator 9/21/2018 Lesson 9 Contents

Real World 9/21/2018

Graph State the domain, range, and x- and y-intercepts. Graph a Square Root Function Graph State the domain, range, and x- and y-intercepts. Since the radicand cannot be negative, identify the domain. Write the expression inside the radicand as  0. Solve for x. The x-intercept is 9/21/2018 Example 9-1a

Make a table of values to graph the function. Graph a Square Root Function cont. Make a table of values to graph the function. 2.83 6 2.55 5 2.23 4 1.87 3 1.14 2 0.71 1 y x 9/21/2018 Example 9-1b

Graph a Square Root Function Cont. Answer: From the graph, you can see that the domain is and the range is y  0. The x-intercept is There is no y-intercept. 9/21/2018 Example 9-1c

x-intercept: 1 y-intercept: none Graph State the domain, range, and x- and y-intercepts. Answer: domain: x  1 range: y  0 x-intercept: 1 y-intercept: none 9/21/2018 Example 9-1d

Graph the function. State the domain and range. Solve a Square Root Problem Physics When an object is spinning in a circular path of radius 2 meters with velocity v, in meters per second, the centripetal acceleration a, in meters per second squared, is directed toward the center of the circle. The velocity v and acceleration a of the object are related by the function Graph the function. State the domain and range. 9/21/2018 Example 9-2a

The function is Make a table of values and graph the function. Solve a Square Root Problem cont. The function is Make a table of values and graph the function. Answer: The domain is a  0 and the range is v  0. a v 1 1.41 2 3 2.45 4 2.83 5 3.16 9/21/2018 Example 9-2b

Solve a Square Root Problem cont. What would be the centripetal acceleration of an object spinning along the circular path with a velocity of 4 meters per second? Original equation Replace v with 4. Square each side. Divide each side by 2. Answer: The centripetal acceleration would be 8 meters per second squared. 9/21/2018 Example 9-2c

a. Graph the function. State the domain and range. Geometry The volume V and surface area A of a soap bubble are related by the function a. Graph the function. State the domain and range. Answer: domain: A  0 range: V  0 9/21/2018 Example 9-2d

b. What would the surface area be if the volume were 94 cubic units? Answer: 100 units2 9/21/2018 Example 9-2e

Graph a Square Root Inequality Graph the related equation Since the boundary is not included, the graph should be dashed. 9/21/2018 Example 9-3a

The domain includes values for So the graph is to the right of Select a point and test its ordered pair. Test (0, 0). false Shade the region that does not include (0, 0). 9/21/2018 Example 9-3b

Graph the related equation The domain includes values for Select a point and test its ordered pair. 9/21/2018 Example 9-3c

Shade the region that includes (4, 1). Test (4, 1). true Shade the region that includes (4, 1). 9/21/2018 Example 9-3d

a. Graph Answer: 9/21/2018 Example 9-3e

b. Graph Answer: 9/21/2018 Example 9-3f

Homework Review 9/21/2018

Homework See Syllabus 5.8 p. 266: 13 – 27 odd and 39. 9/21/2018

Homework - Honors See Syllabus 5.8 p. 266: 13 - 39 odd, 41-43 9/21/2018