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1)Instructions/example vertex to standard form 5
2)Instructions/example for completing the square (standard to vertex form) 5
3) Describe the effect of a,h,k on the parabola's graph 5
4). Unit Question
Description, three unit questions, graph, vertex form solution 5
5) Factoring explanation with example 5
6) Vocab/notation; Reflection on learning. 5

Total 30/30

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Throughout this unit we have learned lots of new vocabulary terms that are used. Some of these new terms are:
-Concave up: When a parabola is facing upwards, and the a value is positive.
-Concave down:When the parabola is facing downwards, and the a value is negative.
-Vertex:The coordinate where the parabolas bottom is located
-x-intercepts:Coordinates where the parabola crosses through the x line.
-y-intercepts: Coordinates where the parabola crosses through the y
-parabola:an open place that is curved, made on a graph with the equation y=(x-h)²+k
-Solutions,roots,zeros: All these terms mean to find the x-intercepts.

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I feel as if I had understood this unit much more than the past units, after a bit of practice, I was able to understand how to go from standard to vertex, and vertex to standard. I now understand the effect of every value on the equation for graphing. One of the only areas where i feel is weak is when it comes to finding the x and y intercepts from vertex or standard form.

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Graph of Unit Formula

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The equation given in this problem was h(t)=160+92t-16t². First you must turn the equation from standard form to vertex form. You should get an answer of h(t)=-16(t-2.875)²+292.25 which is the vertex form. The vertex of the parabola on the graph would be at (2.875,292.25), the max height will be at 292.25 feet in the air, which will occur in 2.875 seconds after the launch. After finding the x intercepts, we would know that the rocket will hit the ground after about

7.149 seconds.

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In order to turn an equation into factored form, a good method to use is the X or cross method, in order to factor, you must have the equation in standard form. You will first make a large x,and put the c value on the top area, and the b value on the bottom area. Now, you must find 2 numbers which will add up to your b value, and multiply to your c value. For example, if you had the equation y=x²+6x+8, you would put the 8 on the top of the x and 6 on the bottom of the x. Now you must find 2 numbers that will add up to 6 and also multiply to equal 8. The 2 numbers in this occasion will be four and two. Now for your final answer, it would be put as y=(x+four)(x+2).

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Standard to Vertex form (Completing the Square)

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Standard to Vertex form (Completing the Square)

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In order to go from standard form to vertex form, you must first factor out the c value from the first two terms. So for example, if the problem in standard form would be y=x²+8x+3, you would first have to factor out the 3, and put it on the side for now. The next step would be to distribute the a from the equation. In this equation, there is no a, so it would be a 1. So you would end up with y= x2 + 8x +3. Next you must add a constant term in to complete the square, in order to do this you must make an area model. In this problem, after making an area model, you will get y=x2 +8x+16-16)+3. Next you must distribute the -16 with the a value in the equation. Since in this equation, the value of a is 1, you will get y=x2 +8x+16)-16+3. Now you will rewrite the equation as a bionomial squared (x-h)2 ,for this problem you would get y=(x+

4)2 -16+3. From here you will just simplify, meaning in this equation, -16+3 and should get y=(x+4)² - 13.

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To go from vertex form, which is y=a(x-h⁾²+k, to standard form, which is , y=ax²+bx+c. To first start, you must use the (x-h)² to create an area model. After creating the area model, you would put the answer you got into the equation for (x-h)² . For example, if we were to turn the equation, y=(x+3)²-10 into standard form, we would start out with making an area model for (x+3)². After creating an area model, you should get an answer of x2 + 6x +9. After getting this answer, you must plug it into the original problem, and get, x2 + 6x +9 - 10. Now you must solve for c and add or subtract the rest, depending on what the problem is. In this example, it would be 9-10, so the final answer for vertex to standard form would be x2 +6x -1

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In this current unit, the main problem was the "Victory Celebration".  The problem was about a varsity soccer team who was celebrating their victory. They had planned to have a firework display, It was going to be on top of a tower. The tower was 160 feet on top, And the rocket was going to be launched and rise initially at 92 feet per second.

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The 3 important questions asked throughout the unit problem are:
-How long will the rocket take to reach the top.
-How high will the rocket go.
-From the moment it launches, how long will it be in the air.

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y=a(x-h)²+k

-The effect of a on a parabola: In the vertex form equation, the variable a usually effects the width of the parabola. It is not like the h or k which effect the x and y coordinates of he parabola. If you were to increase the number from 1, the parabola becomes more narrow. If the number of a is decreased from 1, the parabola becomes wider. The a variable also can effect whether the parabola is concave up or concave down. If a become a negative, it will cause the parabola to be concave down.
examples: y=4(x-2)2
https://www.desmos.com/calculator/mboz5jychu
y=-0.2(x-2)2
https://www.desmos.com/calculator/oejbiry2fo

-The effect of h on a parabola: The variable h in the vertex form equation effects the x coordinates of the parabola's vertex on the graph. The equation shows  (x-h), the subtraction sign also effects the graph, if the equation has a subtraction sign (x-h),  the X coordinate will be positive if it includes addition (x+h), the X coordinate will be negative.
Examples: y=(x-4)²
https://www.desmos.com/calculator/koe7yxhokm

-The effect of k on a parabola
In this equation, k effects the y-coordinates. K becomes the y-coordinate for the vertex of the parabola. If the value of k is negative, the vertex will just go on the negative side of the graph.
examples-
https://www.desmos.com/calculator/pxlermmecu

https://www.desmos.com/calculator/cvvhavudr1