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] |

| | |

| | |

| | |

| | |

| | |

| | |

| | |

| | |

| | |

| | |

| | |

| | |

| | |

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

|10. [pic] |

| |

|Vertex: |

| |

| |

|x |

| |

|y |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

|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] |

| | | |

| | | |

| | | |

| | | |

| | | |

| | | |

| | | |

| | | |

| | | |

|4. [pic] |5. [pic] |6. [pic] |

| | | |

| | | |

| | | |

| | | |

| | | |

| | | |

| | | |

| | | |

| | | |

|7. -[pic] |8. [pic] |9. [pic] |

| | | |

| | | |

| | | |

| | | |

| | | |

| | | |

| | | |

| | | |

| | | |

HW: Simplify each square or cube root. (No Decimals in your answer!)

|1. [pic] |2. [pic] |

| | |

| | |

| | |

| | |

| | |

| | |

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

| | |

| | |

| | |

| | |

| | |

| | |

|5. [pic] |6. [pic] |

| | |

| | |

| | |

| | |

| | |

| | |

|7. [pic] |8. [pic] |

| | |

| | |

| | |

| | |

| | |

| | |

|9. [pic] |10. [pic] |

| | |

| | |

| | |

| | |

| | |

| | |

|11. [pic] |12. [pic] |

| | |

| | |

| | |

| | |

| | |

| | |

|13. [pic] |14. -[pic] |

| | |

| | |

| | |

| | |

| | |

| | |

|15. [pic] |16. [pic] |

| | |

| | |

| | |

| | |

| | |

| | |

|17. [pic] |18. [pic] |

| | |

| | |

| | |

| | |

| | |

| | |

|19. [pic] |20. [pic] |

| | |

| | |

| | |

| | |

| | |

| | |

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

[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

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

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

Google Online Preview   Download