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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