10 - Loudoun County Public Schools



10.3 Solving Quadratic Equations by Graphing

******IMPORTANT******REMEMBER*******IMPORTANT******REMEMBER*******

The solution to any equation can be called any of the following:

__________________, ___________________, __________________, ___________________

To solve a quadratic equation by graphing all you need to do is:

1. __________________ 2. __________________ 3. __________________

A Quadratic Equation can have 3 types of solutions.

Two Solutions One Solutions No Solutions

Example:

1. [pic]

2. [pic]

Solving Quadratic Equations by Graphing on the Calculator

|Solve:  [pic] |Standard 10 x 10 window |

|Since this equation is set equal to zero, the roots will be the locations where the graph crosses the |[pic] |

|x-axis (if the roots are real numbers). | |

|(Remember that the x-axis is really just  y = 0.) | |

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|1.  Set [pic] |[pic] |

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|2.  Use the ZERO command to find the roots --  2nd TRACE (CALC), #2 zero | |

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|3.  Left bound?  Move the spider as close to the root (where the graph crosses the x-axis) as possible.  | |

|Hit the left arrow to move to the "left" of the root.  Hit ENTER.  A "marker" ► will be set to the left | |

|of the root. | |

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|4.  Right bound?  Move the spider as close to the root (where the graph crosses the x-axis) as possible. | |

|Hit the right arrow to move to the "right" of the root.  Hit ENTER.  A "marker" ◄ will be set to the | |

|right of the root. | |

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|5.  Guess?  Just hit ENTER. | |

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|6.  Repeat the entire process to find the second root | |

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|Answer:  | |

|One of the roots is x = -2 | |

|When you repeat the above steps the other root is x = 7 | |

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|So, the answer to the quadratic equation is –2 and 7 | |

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Practice: Solve the Following Equations by Graphing.

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|3. [pic] |4. [pic] |

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Out the Door Activity. This must be turned in prior to leaving the class! Name:

(Work Must be Shown to receive credit!) _____ __________

1. 2.

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5. 6.

7. 8.

10.3 Homework: Solve the Quadratic Equation. For #1-6 you should use the calculator to graph and find the solution. For #7-10 you should graph by hand and find the solution.

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|Solution(s): _______________________ |Zero(s): __________________________ |

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|X-Intercept(s): ____________________ |Root(s): __________________________ |

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|Zero(s): _________________________ |Solution(s): _______________________ |

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|7. [pic] |

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|Vertex: X-Intercepts: |

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|8. [pic] |

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|Vertex: Solutions: |

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|9. [pic] |

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|Vertex: Zeros: |

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|10. [pic] |

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|Vertex: Solutions: |

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-----------------------

133

y

x

10

10

-10

-10

[pic]

x2 – 4 = 0

Which is the solution set for the equation above?

F {-4, 1}

G {-2, 2}

H {-1, 4}

J {0, 4}

Which is a zero of the function f(x) = x2 + 3x – 4?

A -4

B -1

C 3

D 4

Which is the solution set for x2 – 5x – 14 = 0?

F {-7, -2}

G {-7, 2}

H {-2, 7}

J {2, 7}

What are the solutions to the equation below?

[pic][pic]x2 – 12 = 0

A x = -4 or x = 4

B x = -12 or x = 9

C x = -3 or x = 3

D x = 3 or x = 9

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