pre calc review. appendix b-2 ◦ plot points on a graph ◦ find x and y intercepts x intercepts...

B.2 Graphs of Equations B.3 Solving Equations Algebraically and Graphically Pre Calc Review

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Page 1: Pre Calc Review. Appendix B-2 ◦ Plot points on a graph ◦ Find x and y intercepts X intercepts (, 0) Y intercepts ( 0, ) ◦ Graph equations with a

B.2 Graphs of Equations

B.3 Solving Equations Algebraically and Graphically

Pre Calc Review

Appendix B-2◦ Plot points on a graph◦ Find x and y intercepts X intercepts ( , 0) Y intercepts ( 0, )

◦ Graph equations with a calculator and determine the proper window

◦ Use the zoom and trace features on a calculator

You should know how to…

Page 3: Pre Calc Review. Appendix B-2 ◦ Plot points on a graph ◦ Find x and y intercepts X intercepts (, 0) Y intercepts ( 0, ) ◦ Graph equations with a

Determine whether the following are solutions to the given equation:

Equation: y = 10x – 7

Possible solutions: (2, 13) (-1, -3)

Determining Solution Points

Page 4: Pre Calc Review. Appendix B-2 ◦ Plot points on a graph ◦ Find x and y intercepts X intercepts (, 0) Y intercepts ( 0, ) ◦ Graph equations with a

x -2 -1 0 1 2

Graphing an EquationUsing your calculator, graph the following equation:

€

y =1

4x − 3

From the graph, complete the table of values:

Page 5: Pre Calc Review. Appendix B-2 ◦ Plot points on a graph ◦ Find x and y intercepts X intercepts (, 0) Y intercepts ( 0, ) ◦ Graph equations with a

x -2 -1 0 1 2

Graphing an Equation

Using your calculator, graph the following equation:

€

y =6x

x 2 +1

From the graph, complete the table of values:

Page 6: Pre Calc Review. Appendix B-2 ◦ Plot points on a graph ◦ Find x and y intercepts X intercepts (, 0) Y intercepts ( 0, ) ◦ Graph equations with a

Page A43: Match the graphs to the equations for problems 11 – 16

For the next problems, make sure your window is set to standard viewing (-10, 10, 1, -10, 10, 1, 1)

Page A44: Follow directions for problems 47, 48

B-2 Practice Problems

Page 7: Pre Calc Review. Appendix B-2 ◦ Plot points on a graph ◦ Find x and y intercepts X intercepts (, 0) Y intercepts ( 0, ) ◦ Graph equations with a

How do you eliminate fractions in an equation?

ALWAYS check your solution!!!

Solving Equations with Fractions

€

3+3x

4= 2

Page 8: Pre Calc Review. Appendix B-2 ◦ Plot points on a graph ◦ Find x and y intercepts X intercepts (, 0) Y intercepts ( 0, ) ◦ Graph equations with a

Appendix B-3◦ Solve linear equations◦ Set up models to solve problems◦ Translate key words and phrases to equations◦ Use various formulas Perimeter, area, volume, simple interest, compound

interest, distance, temperature◦ Solve word problems

You should know how to…

Page 9: Pre Calc Review. Appendix B-2 ◦ Plot points on a graph ◦ Find x and y intercepts X intercepts (, 0) Y intercepts ( 0, ) ◦ Graph equations with a

Try this one:

Hint: find the LCD

Solving Equations with Fractions

€

x −2=

x +2−6x

x 2 − 4

Page 10: Pre Calc Review. Appendix B-2 ◦ Plot points on a graph ◦ Find x and y intercepts X intercepts (, 0) Y intercepts ( 0, ) ◦ Graph equations with a

How do you eliminate decimals in an equation?

Solving Equations with Decimals

€

3.5x −8 = 0.5x

Page 11: Pre Calc Review. Appendix B-2 ◦ Plot points on a graph ◦ Find x and y intercepts X intercepts (, 0) Y intercepts ( 0, ) ◦ Graph equations with a

Remember there must be 2 cases ~ a positive and a negative.

Solving Absolute Value Equations

€

2 x − 3 = 8

Page 12: Pre Calc Review. Appendix B-2 ◦ Plot points on a graph ◦ Find x and y intercepts X intercepts (, 0) Y intercepts ( 0, ) ◦ Graph equations with a

Find the intercepts for : 2x + 3y = 5

What do we know about ALL y intercepts? What do we know about ALL x intercepts?

Finding x and y intercepts

Page 13: Pre Calc Review. Appendix B-2 ◦ Plot points on a graph ◦ Find x and y intercepts X intercepts (, 0) Y intercepts ( 0, ) ◦ Graph equations with a

Look at page A54 at the different types of equations.

What are the four ways to solve a quadratic equation? (review page A54)

Solving Polynomials Algebraically

Page 14: Pre Calc Review. Appendix B-2 ◦ Plot points on a graph ◦ Find x and y intercepts X intercepts (, 0) Y intercepts ( 0, ) ◦ Graph equations with a

By factoring:

By the square root property:

Solve ~

€

9x 2 −1 = 0

Page 15: Pre Calc Review. Appendix B-2 ◦ Plot points on a graph ◦ Find x and y intercepts X intercepts (, 0) Y intercepts ( 0, ) ◦ Graph equations with a

Solve ~ by factoring

€

x + a( )2−b2 = 0

Page 16: Pre Calc Review. Appendix B-2 ◦ Plot points on a graph ◦ Find x and y intercepts X intercepts (, 0) Y intercepts ( 0, ) ◦ Graph equations with a

Solve ~ by completing the square

€

x 2 +8x +14 = 0

Page 17: Pre Calc Review. Appendix B-2 ◦ Plot points on a graph ◦ Find x and y intercepts X intercepts (, 0) Y intercepts ( 0, ) ◦ Graph equations with a

Solve ~ by quadratic formula

€

9x 2 −12x −14 = 0

Page 18: Pre Calc Review. Appendix B-2 ◦ Plot points on a graph ◦ Find x and y intercepts X intercepts (, 0) Y intercepts ( 0, ) ◦ Graph equations with a

Isolate the radical

Square both sides

Linear or Quadratic?◦ Solve depending upon what type of equation

OR if still a radical present ~ start over at the top

Solving Equations with Radicals

Page 19: Pre Calc Review. Appendix B-2 ◦ Plot points on a graph ◦ Find x and y intercepts X intercepts (, 0) Y intercepts ( 0, ) ◦ Graph equations with a

€

x −10 − 4 = 0

€

x − x −5 =1

Page 20: Pre Calc Review. Appendix B-2 ◦ Plot points on a graph ◦ Find x and y intercepts X intercepts (, 0) Y intercepts ( 0, ) ◦ Graph equations with a

Page A59: 1- 35 odd Page A60: 39 – 91odd Page A61: 93-137 and 167 – 173 odd

Assignment ~

· Ch. 3.5 Polynomial Inequalities l. Graph the following: x-intercepts: (-2 0) o ) y-intercept: (o (—23) Intervals above the x-axi Intervals below the x-axis: —2) Polynomial

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