- x > 0 (Then it has 2 solutions)
- x = 0 (Then it has 1 solution)
- x < 0 (Then it has no solutions)

When given the example

From the equation, we see a= 6, b = 10 and c= -1

Plugging these values into the discriminant, we get:

$latex b2−4ac $

$latex 10^2−4(6)(−1) $

= 124

This is a positive number, so the quadratic has two solutions.

This makes sense if we think about the corresponding graph.

Notice how it crosses the

-axis at two points.In other words, there are two solutions that have a

-value of 0, so there must be two solutions

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- Factoring the equation
- Completing the square
- Quadratic Formula

The areas that I found an still find the most difficult is solving a quadratic equation using the completion of squares method. I find this the hardest out of the three because there is almost no pattern and you tend to do many things to the formula at once. To use any of these three methods you must have the equations equal to zero making it quadratic. The Equation does not always need to have a degree of 2 it can be also solved to the degree of 1. To check your answers plug your (x) value back into the formula and make sure the left side equals the right.

Below you can find examples of the 3 methods of solving for a quadratic formula.

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For Example: x2 + 7x + 12

If you go through the factors of 12 you must find two number that adds to the second value in the expression(7)

1 * 12

2 * 6

3 * 4

4 * 3

Using the factors highlighted in red input them into your expression because 3 + 4 equals to 12

(x + 3) (x +4)

We were also taught what to do if the x2 value is greater than one. Ex: 2×2 + x – 6

To solve this we were introduced to the box method.

- Multiply 6 and 2x and find its factor. (12x) 3 and 4
- Fill in the first value in the top right corner
- Fill in the constant in the bottom right
- Fill in the two factors in the remaining corners
- Lastly find the common factor between the values from up to down and left to right

Claculations:

- 2×2 and 4x – 2x
- -3x and -6 – -3
- 2×2 and -3x – x
- 4x and -6 – 2

Final Answer: (2x – 3) (x + 2)

]]>Still, in this unit, we have not used a single formula because of the fact that throughout this unit we are not allowed to use a calculator.

Below you will see examples of all adding, subtracting, multiplying and dividing of radicals.

]]>Below you will find examples of absolute values and expressions.

In this unit so far we have not used any formulas

]]>**Formulas We Used This Week:**

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Below you can see how the two equations are performed.

**Formulas We Used:**

Sequence:

Series:

**Examples:**

Block A

12 17 2018

Mr Barazzuol

Poem Analysis of *“Where The Sycamore Grew”*

The poem *“Where The Sycamore Grew”*, written by Carrie Richards is a very understandable piece of literature that some viewer may find relatable. The poem presents to the reader a woman, who has just returned to her past home, even seeing this described “sun-yellow” home from a distance gave her instantaneous realizations on how much things have changed. With this great realization the character notices that “The street seems narrower, and the trees are taller.”(3) A side from the amount of meaning this poem has behind it, it also gives off opportunities for possible thematic statements. The poem encompasses many strong topics but the focal point of this poem can be summarized as: life is about leaving things behind and making long-lasting memories out of them. The poem *“Where The Sycamore Grew” *shows us many ways its significance relates to the human life, The speaker exclaims that their first milestone was “a path we laid on a warm summer day/in a place that we knew as our very first home” (28-29)*. * The significance this phrase has is that it help people understand that childhood memories should be remembered forever and not forgotten because you will never re-live that moment Another section the reader is introduced to the significance of this poem is in stanza 1 and our speaker is first introduced to whats left of the childhood home, the speaker notices that “The neighboring orchards have all but disappeared”(6) and this was a place from her childhood that stayed with her forever. The poem uses different types of poetic devices to enhance the reading experience some of which include the use of a metaphor “It’s a path we laid on a warm summer day in a place that we knew as our very first home”* (28-29). * The message this metaphor is trying to convey is “The Path” that the family placed where the first stepping stones into the future of this family. Imagery is commonly used inside this poem, because it is describing such an important mile-stone in a persons life, in this case the woman is describing “Just a small yellow house, with snow-white shutters … that sits ’round the bend, where the sycamore grew…”. The poem “*Where The Sycamore Grew”*, uses hidden symbols to get the reader more engaged on its main focus, the childhood memories. Symbolism is being expressed in lines 7 thought 8, the speaker starts to reflect upon what has changed “But somehow we knew the house would still be there / As if seen from a distance, …yet, still much is the same”(7-8). Inside the poem an example of a simile is being executed while the woman is standing in front of her childhood home and the thoughts and sharp memories began to rush to her head and become”…quickly alive… / like a whirlwind of leaves, in a springtime of lives.”(16-17) The simile is comparing the memories rushing into her vision to a whirlwind that has picked up all of the memories form the back of her head, using this the woman is able to realize that not much has changed over the span of thirty years.

In Conclusion the poem *“Where The Sycamore Grew” *is mainly based off of the life experience, of moving on with your childhood while keeping all those memories you have made, in a sealed box in the back of your mind.

Below is Black Out Poetry that shows what the poem*“Where The Sycamore Grew” *is all about

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