Math 165 Guided Activity to study ahead some concepts from sections 1.1 and 1.2 Name Section Distance and Midpoint Formula

Transcription

1 Math 165 Guided Activity to study ahead some concepts from sections 1.1 and 1. Name Section Distance and Midpoint Formula Use the power point presentation for sections 1.1 and 1. to answer the following They can be found in my website Click on M165; click on Handouts 1. Write the distance formula; show an appropriate sketch. Write the midpoint formula; label the midpoint on the sketch of part (1). 3. In a coordinate system, plot the points A(-, 5) and B(3, -5). Use the formulas to determine the distance AB and the coordinates of the midpoint of the segment AB. Section 1. Intercepts and Symmetry 4. How do you find the x-intercept of an equation? 5. How do you find the y-intercept of an equation? 6. Find the x- and the y-intercepts of the equation x 5y = 3. Show ALL work. Show a rough sketch on this paper; label intercepts. 7. Draw a complete graph so that it has a) x-axis symmetry. b) y axis symmetry c) Origin symmetry 1

2 Section 1.1 Graphing equations with the calculator 8. Practice the following calculator skills. Bring your questions to class Graph x + 3 y = 17 Solve for Y Enter equation into Y1 (use parenthesis around fractions) Press Y= Open a window to see the graph Press ZOOM 6:ZStandard to open standard window Press WINDOW and explore the values of the standard window Is this window showing the x- and y-intercepts (a complete graph) of the equation? Press ZOOM 4:Zdecimal to open the decimal window Press WINDOW and explore the values of this window Is this window showing the x- and y-intercepts (a complete graph) of the equation? Press WINDOW and enter your own values Press GRAPH to see the graph Explore the table for this equation AUTO mode Press nd WINDOW [TBLSET] to set up the table Select AUTO mode Press nd GRAPH [TABLE] to explore the table Scroll up and down Now explore the ASK mode of the table Press nd WINDOW [TBLSET] to set up the table Select ASK mode Press nd GRAPH [TABLE] to access the table Type a value for x and press ENTER Determine the y-intercept of an equation with the calculator Press nd TRACE [CALC] Select 1:value Type 0 for x and press ENTER Determine the x-intercept(s) (or zeros) of an equation with the calculator Press nd TRACE [CALC] Select :zero Arrow left/right and press ENTER when you are to the left of the zero Arrow left/right and press ENTER when you are to the right of the zero Arrow close to the zero and press ENTER to select your GUESS

3 Math 165 Guided Activity to study ahead some concepts from section 1.3 Section 1.3 Solving Equations, Graphical Approach Read the book or the power point presentations for this section. Name Solving equations using the intersection of graphs method: 1) Use the intersection of graphs method to solve the following equation. 3x 8= x Here are the steps to accomplish this: a) Enter the left hand side of the equation in Y1 of your calculator. b) Enter the right hand side of the equation in Y of your calculator. c) Press ZOOM, select 6:Standard to graph d) Press nd TRACE to access the CALC menu, select 5:Intersect. Press ENTER three times to get the point of intersection. e) The answers are the x-coordinates of the points of intersection Answers: x = and x = Show a neat graph, label solutions on the graph. Solving equations using the x-intercept method: ) Use the x-intercept method to solve the following equation. 3x 8= x Here are the steps to accomplish this: a) Set the equation equal zero b) Enter the left hand side of the equation in Y1 c) Let Y = 0 (this is the right hand side of the equation) d) Use the intersect option in the CALC menu to find the two x-intercepts. e) IN CLASS WE WILL LEARN to use THE ZERO option to find the solutions Answers: x = and x = Show a neat graph, label solutions on the graph. 3

4 Math 165 Guided Activity to study ahead some concepts from section 1.5 Name Section Circles Use the power point presentation for section 1.5 to answer the following It can be found in my website Click on M165; click on Handouts 1) Write the standard form of an equation of a circle with radius r and center C(h, k). ) Write the standard form of an equation of a circle with radius r and center C(0, 0). 3) Write the standard form of an equation of a circle with radius and center C(0, 0). 4) Write the standard form of an equation of a circle with radius 5 and center C(, -3). 5) Write the general form of the equation of a circle. 6) Use the equation from part (4), perform all the operations (FOIL and combine like terms) and set it equal zero to obtain the general form of the equation of the circle. 4

5 Math 165 Section 1.1 Distance and Midpoint Formulas practice Page 16 our book Page 17, our book 5

6 Math 165 Section 1.5 Circles practice 1) Write the equation of the circle with center C(5, -8) and radius 3. a. Answer in standard form. b. Answer in general form. c. Sketch graph by hand. d. What equations do you enter in the editor of the calculator to graph? ) Given the equation of a circle in general form, find the coordinates of the center and the radius. 3) Given the coordinates of a diameter of a circle, write the equation of the circle in both forms. 4) Similar to #51 and #5, page 51, our book - In 008, the Singapore Flyer opened as the world s largest Ferris wheel. It has a maximum height of 165 meters and a diameter of 150 meters, with one full rotation taking approximately 30 minutes. Find an equation for the wheel if the center of the wheel is on the y-axis. 5) #53, page 51, our book - Weather Satellites: Earth is represented on a map of a portion of the solar systems so that its surface is the circle with equation. A weather satellite circles 0.6 unit above Earth with the center of its circular orbit at the center of the Earth. Find the equation for the orbit of the satellite on this map. 6

7 = 4 6) a) Graph by hand: ( x ) ( y ) b) What functions do you enter in the Y= of the calculator to graph the circle? c) Find the x- and y-intercepts 7) Find the equation of the circle if the endpoints of a diameter are A(-5, 8) and B(4, -). 7