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This was a continuation lesson on factoring and getting used to the area model and the diamond diagram which would later give us the factored form of our quadratic. The reason I liked this lesson was solely because I got a better understanding of factoring and why it’s important we know both the sum and the product of a quadratic formula. Also the only reason I did get the hang of it was because of the color coding; by learning this , this made graphing the quadratic easier and finding all the necessary things needed when we graph it more understanding rather than tricky.

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Describe WHY this was your favorite lesson in at least 3 sentences. (don’t just say because it was easy that’s why you liked that lesson). Upload a picture of that lesson from your notebook.

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Answer the essential question from your favorite lesson (3 or more sentences). If you do not have the essential question written down ask a friend if they wrote it down. Include a visual from internet that relates to it.

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Describe in 3 or more sentences how a topic in this chapter can be applied to the real world.  Include a visual from the internet that relates to it!

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I didn’t realize this until late in the quarter BUT the fastest method to get what’s inside the box without using the diamond is to keep the x squared in the problem and the y intercept the same but the only thing that’s going to change is the middle variable of x. So , in this example we have 11x we break it apart and we add what gives us 11x (6x+5x) and we put them in the box. That is how we save time on solving a quadrics factored form.

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Quadratics in the real world are used to make rollercoasters and with this, a quadratic equation can tell us how far a rollercoasters train can go in terms of going on multiple loops in one session. Without a quadratics factored form, we can’t know if the parabola will have a high or low vertex.

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At first, this lesson seemed so confusing because why is there a need for letters and numbers to be mixed together; I got the basic jist of it and it was basically you solve the square root of a undefined number which are usually negative. With the idea of imaginary numbers you just add an i to fix the previous unsolvable problem.

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Imaginary numbers is when you have a situation in which the square root is negative; imaginary numbers introduce us with the solution to that previous unsolvable equation by square rooting the number like normal and adding the i at the end of the solution.

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Linear graphs in the real world can show us an increase or decrease in data in many ways (like applying them to sales in a year or purchased of specific stuff over a time period)
Quadratic graphs help us measure the highest point in a curved item ( we use this for roller coaster physics and how high a roller coaster can go)
Exponential: this graph is used for showing us the growth and decay of something (we can compare things like gas processing with this)

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I liked this one because it didn’t require much due to the fact we used numbers from the center and the radius and we used them to find out how the circle would be placed (center) and how wide it would be (radius). The equation for it wasn’t hard and the on,y thing you did have to watch out was changing the signs when it came to the x-h^2.

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The equation to a circle equation is what the final outcome is from both the center and the radius. We would take the radius and square it and have our 2 initial center numbers changed if necessary (h variable) but we would leave the second number alone without any changes (k).

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By knowing the radius and the center of a circle, we know how the circle will occupy in terms of length and how it will move based on the given things. With a Ferris wheel , we can see it turns and moves at certain angles and has carts distributed to meet its radius and center.