Math 165 – Guided Activity to study ahead some concepts from sections 1.1 and 1.2
Name______
Section 1.1 - Distance and Midpoint Formula
Use the power point presentation for sections 1.1 and 1.2 to answer the following
They can be found in my website http://faculty.montgomerycollege.edu/maronne/
Click on M165; click on Handouts
- Write the distance formula; show an appropriate sketch
- Write the midpoint formula; label the midpoint on the sketch of part (1).
- In a coordinate system, plot the points A(-2, 5) and B(3, -5). Use the formulas to determine the distance AB and the coordinates of the midpoint of the segment AB.
Section 1.2 – Intercepts and Symmetry
- How do you find the x-intercept of an equation?
- How do you find the y-intercept of an equation?
- Find the x- and the y-intercepts of the equation 2x – 5y = 23. Show ALL work. Show a rough sketch on this paper; label intercepts.
- Draw a complete graph so that it has
a) x-axis symmetry.b) y axis symmetryc) Origin symmetry
Math 165 – Section 1.1 – Distance and Midpoint Formulas – practice
Page 16 – our book
Math 165 – Section 1.1 – Distance and Midpoint Formulas – practice
Page 17, our book
Section 1.1 – Graphing equations with the calculator
These are skills you should be familiar with from a prior class – Review ON YOUR OWN
- Practice the following calculator skills. Bring your questions to class
Graph 2 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:ZStandardto 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:Zdecimalto 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 2nd WINDOW [TBLSET] to set up the table
Select AUTO mode
Press 2nd GRAPH [TABLE] to explore the table
Scroll up and down
Now explore the ASK mode of the table
Press 2nd WINDOW [TBLSET] to set up the table
Select ASK mode
Press 2nd 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 2nd 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 2nd TRACE [CALC]
Select 2: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
Math 165 – Guided Activity to study ahead some concepts from section 1.3Name ______
These are skills you should know from a prior class
Section 1.3 – Solving Equations, Graphical Approach
Read the book or the power point presentations for this section.
Solving equations using the intersection of graphs method:
1) Use the intersection of graphs method to solve the following equation.
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 Y2 of your calculator.
c) Press ZOOM, select 6:Standard to graph
d) Press 2nd 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:
2) Use the x-intercept method to solve the following equation.
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 Y2 = 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.
Math 165 – Guided Activity to study ahead some concepts from section 1.5
Name ______
Section 1.5 - Circles
Use the power point presentation for section 1.5 to answer the following
It can be found in my website http://faculty.montgomerycollege.edu/maronne/
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).
2) 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 2 and center C(0, 0).
4) Write the standard form of an equation of a circle with radius 5 and center C(2, -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.
Math 165 – Section 1.5 – Circles – practice
7) Write the equation of the circle with center C(5, -8) and radius 3.
- Answer in standard form.
- Answer in general form.
- Sketch graph by hand.
- What equations do you enter in the editor of the calculator to graph?
8) a) Graph by hand:
b) What functions do you enter in the Y= of the calculator to graph the circle?
c) Find the x- and y-intercepts
9) Similar to #51 and #52, page 51, our book - In 2008, 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.
Math 165 – Section 1.5 – Circles – practice
10) Find the equation of the circle if the endpoints of a diameter are A(-5, 8) and B(4, -2).
11) Given the equation of a circle in general form, find the coordinates of the center and the radius.
a)
b)
c)
12) #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.
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