Chapter 10 Review



Chapter 10 Review

10.1+10.2 Graph Quadratic Functions

• Use your calculator

• Identify the Vertex (ordered pair)

• Identify the Axis of Symmetry (x = )

y = 2x2 + 2x + 1 Vertex: ______________________

Axis of Symmetry: _____________

Graph:

10.3 Solve Quadratic Functions by Graphing

• Use your calculator

• Find the x-intercepts of the graph

• If it does not cross the x-axis…then there is no solution.

x2 – 2x = 8 Solution(s): ______________________

Graph:

Two Solutions One Solutions No Solutions

11.2 Simplify the Square or Cubic Root

• Factor the radicand using a factor tree

• Circle “pairs” of numbers for square roots or “three of a kinds” for cubes

• Remove a “representative” of each “pair” or “three of a kind”

• Multiply to simplify

a. [pic] b. [pic]

10.4 Use Square Roots to Solve Quadratic Equations (only works for: ax2 + c = 0)

• Get the x2 by itself on one side of the equations and take the square root of both sides.

• Remember if x2= positive number…there are two answers… (

• Remember if x2= 0…there is one answer… 0

• Remember if x2= negative number…there are no answers…no solution

a. [pic] b. [pic]

Solve a quadratic by Factoring

• Get everything on one side of the equation so ax2+bx+c=0

• Factor the quadratic, if possible.

• Set each factor = 0 and solve.

a. [pic] b. [pic]

10.6 Using the Quadratic Formula to Solve Quadratic Equations [pic]

• Get everything on one side of the equation so ax2+bx+c=0

• If [pic]is positive…two answers

• If [pic]is zero…one answer

• If [pic]is negative…no answers

a. 2x2 – 3x + 1 = 0 b. x2 – 2x + 2 = 0

|L1 |L2 |

|6.3 |215 |

|6.9 |248 |

|6 |185 |

|6.5 |228 |

|6.3 |205 |

|6.3 |265 |

|7 |263 |

|6.8 |235 |

Linear and Quadratic Regression

To enter data to be graphed:

1. Press Stat then Edit. Enter.

2. Enter your data into lists L1 and L2.

3. Press Stat Plot (i.e. 2nd and y=). Choose #1. Press Enter.

4. Turn plot On.

5. Press Zoom. Choose #9.

6. Does it follow a linear or quadratic trend? _______________

To draw a best-fit line/curve ( the calculator considers this a “Linear Regression or Quadratic Regression.”):

1. To go to your home screen (press 2nd and Mode).

2. Press Stat then right arrow to Calc.

3. Choose #4, “LinReg (ax+b)” (because this line looks linear). (If it looked quadratic…choose #5)

4. Enter.

5. The values shown are the slope (“a” is m) and the y-intercept (b).

The line of best fit for the above data is y = ________x + _________

The number of reported AIDS cases in Virginia from the years 1990-1999 is shown below. Let x be the number of years since 1990 and y be the number of reported cases.

|Year |1990 |1991 |

|1973 |3 |26.2 |

|1980 |10 |19.2 |

|1987 |17 |16.6 |

|1993 |23 |18.8 |

|1997 |27 |19.5 |

20.

a. Does this data look Linear or Quadratic?

b. What is the Line/Curve of Best Fit?

c. How many hours of Leisure time would you expect someone in the year 2000 to have had (let x = 30)?

21. 22.

23.

24.

25.

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

Use the X (years since 1970) for L1 and Hours for L2.

144

145

The stress distribution on a structure is given by s = 2x2 + 4x – 30 where s is stress in pounds per square inch and x is the distance in feet from a reference point. At what distance is the stress equal to 0?

A 3 ft

B 5 ft

C 6 ft

D 12 ft

One factor of 5x2 + 13x – 6 is ---

A 5x – 6

B 5x – 1

C 5x – 2

D 5x – 3

Put a Check next to the function(s) with exactly one zero! You may have more than one answer!

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