Solving Quadratic Equations by Graphing



Solving Quadratic Equations by Graphing

§6.1

Quadratic Function

[pic]

Write each in quadratic form.

Example 1

[pic]

Example 2

Graph [pic]

Example 3

An arrow is shot upward with an initial velocity of 64 [pic]. The height of the arrow h(t) in terms of the time t since the arrow was released is h(t) = [pic]. How long after the arrow is released does it reach maximum height? What is the height?

Example 4

Solve [pic] by graphing.

2 real solutions 1 real solution 0 solutions

Pg 338, 8 – 42

Solving Quadratic Equations by Factoring

§6.2

Example 1 Example 2

[pic] [pic]

Example 3 Example 4

[pic] [pic]

Example 5 Example 6

[pic] [pic]

Pg 344, 5-33 odd

Solving Quadratic Equations by Completing the Square

(Opposite of Perfect Square Trinomial)

§6.3

Example 1

Find the value of c that would make [pic] a perfect square.

Solve by completing the square.

Example 2 Example 3

[pic] [pic]

Example 4 Example 5

[pic] [pic]

Pg 350, 7-35 odd

The Quadratic Formula and the Discriminant

§6.4

Solve by Completing the Square

[pic]

Quadratic Formula

[pic]

Example 1 Example 2

[pic] [pic]

Example 3 Example 4

[pic] [pic]

Example 5

[pic]

Discriminant

[pic]

*Describes the nature of the roots*

|Value |Perfect Square |Roots |Graph |

|[pic] > 0 | | | |

|[pic] > 0 | | | |

|[pic] < 0 | | | |

|[pic] = 0 | | | |

Find the value of the discriminant and describe the nature of the roots.

Example 6 Example 7

[pic] [pic]

Pg 357, 8-36 even

Sum and Product of Roots

§6.5

x = 4 x = -7

Writing Equations (Quadratic)

1. [pic]

2. [pic]

Write a quadratic equation that has the following roots.

Example 1 Example 2

[pic] and 5 [pic] and [pic]

Example 3 Example 4

7 – 2i and 7 + 2i [pic] and [pic]

Solve each equation and check using the sum and product of the roots.

Example 5

[pic]

Pg 362, 5-39

Analyzing Graphs of Quadratic Functions

§6.6

Quadratic Equations

[pic]

Vertex = (h, k)

Axis of Symmetry: x = h

Example 1

Name the vertex and the axis of symmetry for the graph of

f(x) = [pic]. How is the graph of this function different from the graph of f(x) = [pic]?

How does a in [pic] affect a parabola?

a. [pic]

b. [pic]

c. [pic]

d. [pic]

Example 2

Graph f(x) = [pic]. Name the vertex, axis of symmetry, and direction of the opening.

Example 3

Write [pic] in [pic] form.

Example 4

Write the equation of the parabola that passes through the points at

(9, -3), (6, 3), and (4, 27).

Pg 372, 1-45 odds

Graphing Quadratic Inequalities

§6.7

Example 1 Example 2

Graph [pic] Graph [pic]

Example 3

Solve [pic] by Graphing.

Example 4

Solve [pic] by Factoring.

Pg 381, 7-49 odds

Standard Deviation

§6.8

Standard Deviation (SD or [pic]) – a measure of variation, or spread, which measures how much each value in a set of data differs from the mean.

[pic]

|Team |1994 Average |Team |1994 Average |

|Arizona |27.69 |LA Rams |29.13 |

|Atlanta |27.00 |Miami |29.65 |

|Buffalo |33.73 |Minnesota |29.79 |

|Chicago |32.23 |New England |34.34 |

|Cincinnati |28.43 |New Orleans |26.71 |

|Cleveland |27.27 |NY Giants |35.59 |

|Dallas |32.85 |NY Jets |25.00 |

|Denver |32.34 |Philadelphia |40.00 |

|Detroit |30.04 |Pittsburgh |30.99 |

|Green Bay |26.13 |San Diego |33.86 |

|Houston |31.88 |San Francisco |39.75 |

|Indianapolis |26.48 |Seattle |28.00 |

|Kansas City |29.16 |Tampa Bay |29.57 |

|LA Raiders |31.32 |Washington |35.70 |

Graphing Calculator

1. Clear List – STAT, 4, 2nd [pic], enter

2. STAT, EDIT, enter all values in [pic]

3. STAT, CALC, 1-Var Stats, enter twice.

4. To clear again: STAT, 4, 2nd STAT, enter twice.

Pg 389, 5-20 skip 9

The Normal Distribution

§6.9

Frequency distribution – shows how data are spread out over the range of values.

Histogram – a bar graph that displays a frequency distribution.

Normal Distribution (bell curve) – a symmetric curve which indicates that the frequencies are concentrated around the center portion of the distribution.

Example 1

The useful lives of 10,000 batteries are normally distributed. The mean useful life is 20 hours, and the SD is 4 hours.

a. Sketch a normal curve.

b. How many batteries will last between 16 and 24 hours?

c. How many batteries will last less than 12 hours?

d. What is the probability that a battery will last between 16 and 28 hours?

Skewed Distribution – a distribution curve that is not symmetric.

High left, tail right: + skewed

High right, tail left: - skewed

Positively Skewed

Pg 395, 5-17

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download