LearnZillion Notes:.

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LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

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LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

Are 4(5x + 2) and 4(5x) +4(2) equivalent expressions?

Rule: double the number and add 1

How do you find the length of sides and then use that to find perimeter and area when only given ordered pairs? For example: (4,1) (4,-4) (-6,1) (-6,-4)

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

SAY: Both ratios have a 1/2 relationship because ½ of 10 is 5 and ½ of 12 is 6.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is our lesson objective. Keep it as short and student-friendly as possible. Put what they will learn in green and then how they’ll.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

For example, how can you use exponents to write

7 x 2 5 LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try.

For example: Equilateral Triangle All sides are congruent. All angles are 60˚. LearnZillion Notes: --Some lessons may build off of previous lessons.

For example, what would the value of this numerical expression be?

2 3 = …. LearnZillion Notes:

How do you find the volume of a sphere?

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

Objectives Transform quadratic functions.

LearnZillion Notes: --This is our lesson objective. Keep it as short and student-friendly as possible. Put what they will learn in green and then how they’ll.

For example: Does the function

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

Find the first six multiples of 8.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

Find the first six multiples of 4.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

0.7 = ? ? LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?”

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

Ticket in the Door a = -7 3 d – 19 = 4 20 Agenda Ticket in the Door

1 4 = 2 8 LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

-Read question -”Would we say that it is very likely? Unlikely? Impossible?”

0.73 = ? ? LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?”

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

For Example: Does 2:3 = 7:9 ? In the example, I will draw an equal sign between the two ratios and then draw a line through it to illustrate equal or not.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

Input Output LearnZillion Notes:

x ft 30 ft 40 ft LearnZillion Notes:

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

1 2 ÷ 4 LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?”

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --Some lessons may build off of previous lessons. In those cases, it may be helpful to include one or more review slides.

For example: How do you show an increase of 12% over the original cost, if the original cost is $x? LearnZillion Notes: --This is your hook. Start with.

I wonder…2 _ 1 2 ? LearnZillion Notes:

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

Presentation transcript:

LearnZillion Notes:

LearnZillion Notes:

LearnZillion Notes: You already know that the function f(x) = x2 is a parabola with the origin as its vertex.

f(x)= x2 +k is a vertical translation of f(x)= x2 by k units. LearnZillion Notes: You also know that a function in the form f(x)= x2 +k is a vertical translation of the function f(x)= x2 by k units. For example, f(x)= x^2+3 is a vertical translation of the function x^2 of 3 units in the positive y direction. This means that all the points, including the vertex, are vertically translated by positive 3 units.

f(x)= (x-h)2 is a horizontal translation of f(x)=x2 by h units. LearnZillion Notes: You also know that a function in the form f(x)= (x-h)2 is a horizontal translation of the function f(x)= x2 by h units. For example, f(x)= (x-2)^2 is a horizontal translation of the function x^2 of 2 units in the positive x direction. This means that all the points, including the vertex, are horizontally translated by positive 2 units.

f(x) = x2 -8x + 21 f(x) = (x2-8x +16) +21 -16 f(x) = (x-4)2 + 5 LearnZillion Notes: You also know how to take an equation written in standard form and rewrite it by completing the square. For example, f(x) = x2 -8x + 21 can be rewritten as f(x) = (x-4)2 + 5 This form of the a quadratic equation is called the vertex form. In general vertex form is written as f(x) = (x-h)2 + k We’ll talk a little more about why it is called vertex form in just a minute.

f(x)= x2 -6x + 13 f(x)= (x-3)2 + 4 LearnZillion Notes: Let’s look at the function f(x)= x2 -6x + 13. Can you look at this function written in standard form and tell exactly where it’s vertex is located on a coordinate plane? It is extremely difficult to do so. This function can be re-written in vertex form as f(x)= (x-3)2 + 4. Why is this called the vertex form? Let’s look at what we know. We know that the x-3 inside the parentheses means the vertex translates positive 3 units horizontally from the origin. We also know that the constant term of +4 means the vertex translates positive 4 units. When we combine this into one translation from the origin, we get a new vertex of (3, 4) Take a look at the graph of this function and then look back at the function written in vertex form. We can actually see the vertex revealed in the structure of the equation. Let’s look at one more example to see if you can predict the location of the vertex.

f(x)= x2 +4x + 1 f(x)= (x+2)2 -3 LearnZillion Notes: Let’s look at the function f(x)= x2 +4x + 1. Can you look at this function written in standard form and tell exactly where it’s vertex is located on a coordinate plane? Now try it written in vertex form: f(x)= (x+2)2 -3. Can you see the location of the vertex? The x+2 in parentheses tells us we have a horizontal translation of -2 and the constant term of -3 tells us that we have a vertical translation of -3 so the new vertex is (-2, -3) Again, looking at the graph of this function we can confirm that (-2,-3) is indeed the vertex of this function.

For example, the vertex of f(x) = (x-h)2 + k For example, the vertex of f(x) = (x-4)2 + 3 must be (-4, 3) Actual vertex: (4, 3) LearnZillion Notes: A common mistake is to think that the vertex has the same sign as h in the vertex form rather than the opposite sign of h in f(x) = (x-h)2 + k For example, it would be easy to think the vertex of f(x) = (x-4)2 + 3 is (-4, 3). This is a mistake, however, since the actual vertex is (4,3).

LearnZillion Notes: --

Solution: f(x) = (x+3)2 -5 vertex: (-3, -5) LearnZillion Notes: The leading coefficient is positive so the function will have a minimum value. We can confirm this is true by taking a quick look at the graph of the function.

Solution: f(x) = 2(x-1)2 +3 vertex: (1, 3) LearnZillion Notes: The leading coefficient is positive so the function will have a minimum value. We can confirm this is true by taking a quick look at the graph of the function.

LearnZillion Notes:

LearnZillion Notes: --”Quick Quiz” is an easy way to check for student understanding at the end of a lesson. On this slide, you’ll simply display 2 problems that are similar to the previous examples. That’s it! You won’t be recording a video of this slide and when teachers download the slides, they’ll direct their students through the example on their own so you don’t need to show an answer to the question.