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B.2 Graphs of Equations
B.3 Solving Equations Algebraically and Graphically
Pre Calc Review
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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…
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Determine whether the following are solutions to the given equation:
Equation: y = 10x – 7
Possible solutions: (2, 13) (-1, -3)
Determining Solution Points
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x -2 -1 0 1 2
y
Graphing an EquationUsing your calculator, graph the following equation:
€
y =1
4x − 3
From the graph, complete the table of values:
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x -2 -1 0 1 2
y
Graphing an Equation
Using your calculator, graph the following equation:
€
y =6x
x 2 +1
From the graph, complete the table of values:
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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
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How do you eliminate fractions in an equation?
ALWAYS check your solution!!!
Solving Equations with Fractions
€
x
3+3x
4= 2
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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…
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Try this one:
Hint: find the LCD
Solving Equations with Fractions
€
1
x −2=
3
x +2−6x
x 2 − 4
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How do you eliminate decimals in an equation?
Solving Equations with Decimals
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3.5x −8 = 0.5x
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Remember there must be 2 cases ~ a positive and a negative.
Solving Absolute Value Equations
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2 x − 3 = 8
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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
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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
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By factoring:
By the square root property:
Solve ~
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9x 2 −1 = 0
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Solve ~ by factoring
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x + a( )2−b2 = 0
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Solve ~ by completing the square
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x 2 +8x +14 = 0
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Solve ~ by quadratic formula
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9x 2 −12x −14 = 0
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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
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x −10 − 4 = 0
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x − x −5 =1
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Page A59: 1- 35 odd Page A60: 39 – 91odd Page A61: 93-137 and 167 – 173 odd
Assignment ~