Lesson 11
10.1-10.3 Graphing Review
Important Vocabulary to know!
A Quadratic Function written in standard form looks like:
Name 3 other words that mean the same thing as the Solution to an equation…
_______________________, ________________________, ________________________
The graph of a Quadratic Function is called a _____________________.
The formula for the vertex is:
If the vertex is on the top of the parabola it is called a __________________.
If the vertex is on the bottom of the parabola it is called a ____________________.
A quadratic function can have ___________, __________ or __________ solutions.
Graph the Following Quadratics and Find the Zeros of the Function.
|1. [pic] |2. [pic] |
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|Solution(s): _______________________ |Zero(s): __________________________ |
|10. [pic] |
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|Vertex: |
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|y |
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|Root(s): ______________________ |
Simplifying Square and Cubic Roots
When we raise a number to the second power we ‘square’ that number. Squaring a number means to multiply the number by itself. The square of an integer is called a perfect square.
List the first 10 perfect squares. Find the square roots.
12 ________ 62 ________
22 ________ 72 ________
32 ________ 82 ________
42 ________ 92 ________
52 ________ 102 ________
If [pic], then x = ____ or ____
If [pic], then x = ____ or ____ Only use [pic] if you are solving for x!
The symbol [pic]is called a radical sign and always represents a non-negative square root. The number under the radical sign is called the radicand (or argument). Together the radical sign and the radicand is called a radical and an algebraic expression containing a radical is called a radical expression.
How do you find the square root of a number that is not a perfect square? You can either estimate or simplify them.
Estimate [pic] [pic] [pic] [pic]
3 ? 4
Based on this information, you know [pic] is between 3 and 4. Use the square root key on the calculator to find a closer approximation.
Estimate the following values (Between which two whole numbers).
a. [pic] b. [pic] c. [pic]
Note:
You cannot have a negative number under the square root sign. For example:
[pic]is not a real number since you cannot square any number and get a negative number.
Rules of Simplification
|[pic] |
Simplifying square root expressions without using decimals
• Factor the radicand using a factor tree
• Circle “pairs” of numbers
• Remove a “representative” of each “pair”
• Multiply to simplify
1. [pic] or [pic]
2. [pic]
3. [pic]
Cube Roots
The cube root of 8 is written[pic], since [pic](which means 2[pic]2[pic]2 = 8).
The cube root of -8 is written [pic] because -2[pic]-2[pic] -2 = -8.
A Few Perfect Cubes… Find the Cube Root:
Something to think about:
1) [pic] 2)[pic] 3)[pic]
Simplifying cube root expressions without using decimals
• Factor the radicand using a factor tree
• Circle “three of a kinds” of numbers
• Remove a “representative” of each “set of three”
• Multiply to simplify
1. [pic]
2. [pic]
Examples: Simplify each Square or Cube Root.
|1. [pic] |2. [pic] |3. -[pic] |
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|4. [pic] |5. [pic] |6. [pic] |
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|7. -[pic] |8. [pic] |9. [pic] |
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HW: Simplify each square or cube root. (No Decimals in your answer!)
|1. [pic] |2. [pic] |
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|3. [pic] |4. [pic] |
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|5. [pic] |6. [pic] |
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|7. [pic] |8. [pic] |
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|9. [pic] |10. [pic] |
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|11. [pic] |12. [pic] |
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|13. [pic] |14. -[pic] |
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|15. [pic] |16. [pic] |
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|17. [pic] |18. [pic] |
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|19. [pic] |20. [pic] |
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-----------------------
[pic]= [pic]________ [pic]=[pic]_______[pic]
[pic]= [pic]________ [pic]=[pic]_______
[pic]= [pic]________ [pic]=[pic]________
[pic]= [pic]________ [pic]=[pic]________
[pic]=[pic]________ [pic]=[pic]_______
Circle Pairs since you are simplifying a square root
Notice that you can have a negative under the cube root sign…the answer is then negative.
13 = ______ 43 = ______
23 = ______ 53 = ______
33 = ______ 63 = ______
[pic]= ______ [pic]= ______
[pic]= ______ [pic]= ______
[pic]= ______ [pic]= ______
Circle ‘Three of a Kinds’ since you are simplifying a cube roots
Final Answer!
135
y
x
10
10
-10
-10
y
x
10
10
-10
-10
y
x
10
10
-10
-10
136
137
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