COMPLETING THE SQUARE AND VERTEX FORM UNIT 2

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COMPLETING THE SQUARE AND VERTEX FORM UNIT 2 DAY 10

COMPLETING THE SQUARE AND VERTEX FORM UNIT 2 DAY 10

A-SSE. A. 2: I can use the structure of an expression to identify ways

A-SSE. A. 2: I can use the structure of an expression to identify ways to rewrite it. F-IF. 8. a: I can use the process of factoring and completing the square in a quadratic function to show zeroes, extreme values, symmetry of the graph, and interpret these in terms of the context.

I can solve a quadratic equation using the completing the square method. Watch Instructional

I can solve a quadratic equation using the completing the square method. Watch Instructional Video & Take Notes https: //learnzillion. com/lesson_plans/4988

Watch. OUT! Preventing Errors The leading coefficient term of the trinomial must be 1.

Watch. OUT! Preventing Errors The leading coefficient term of the trinomial must be 1. When the leading coefficient is not 1, check to see if you can factor out the value from the other remaining terms. Common Errors Remember to think carefully about the difference between multiplying a quantity by 2 and squaring the quantity.

GUIDED PRACTICE U 2 A 10 EXAMPLE 1

GUIDED PRACTICE U 2 A 10 EXAMPLE 1

GUIDED PRACTICE U 2 A 10 EXAMPLE 1

GUIDED PRACTICE U 2 A 10 EXAMPLE 1

GUIDED PRACTICE U 2 A 10 EXAMPLE 2

GUIDED PRACTICE U 2 A 10 EXAMPLE 2

GUIDED PRACTICE U 2 A 10 EXAMPLE 2

GUIDED PRACTICE U 2 A 10 EXAMPLE 2

GUIDED PRACTICE U 2 A 10 EXAMPLE 3

GUIDED PRACTICE U 2 A 10 EXAMPLE 3

GUIDED PRACTICE U 2 A 10 EXAMPLE 3

GUIDED PRACTICE U 2 A 10 EXAMPLE 3

GUIDED PRACTICE U 2 A 10 EXAMPLE 4

GUIDED PRACTICE U 2 A 10 EXAMPLE 4

GUIDED PRACTICE U 2 A 10 EXAMPLE 4

GUIDED PRACTICE U 2 A 10 EXAMPLE 4

INDEPENDENT PRACTICE U 2 A 10 EXAMPLE 5

INDEPENDENT PRACTICE U 2 A 10 EXAMPLE 5

INDEPENDENT PRACTICE U 2 A 10 EXAMPLE 5

INDEPENDENT PRACTICE U 2 A 10 EXAMPLE 5

INDEPENDENT PRACTICE U 2 A 10 EXAMPLE 6

INDEPENDENT PRACTICE U 2 A 10 EXAMPLE 6

INDEPENDENT PRACTICE U 2 A 10 EXAMPLE 6

INDEPENDENT PRACTICE U 2 A 10 EXAMPLE 6

INDEPENDENT PRACTICE U 2 A 10 EXAMPLE 7

INDEPENDENT PRACTICE U 2 A 10 EXAMPLE 7

INDEPENDENT PRACTICE U 2 A 10 EXAMPLE 7

INDEPENDENT PRACTICE U 2 A 10 EXAMPLE 7

CHECKING FOR UNDERSTANDING… What does a quadratic equation in vertex form reveal about the

CHECKING FOR UNDERSTANDING… What does a quadratic equation in vertex form reveal about the function? Why do most students prefer to graph a function when it is in vertex form?

Given a quadratic function in standard form, , I can use the completing the

Given a quadratic function in standard form, , I can use the completing the square method to rewrite the function in vertex form, , where (h, k) is the vertex of the quadratic function.

GUIDED PRACTICE U 2 A 10 EXAMPLE 8 Step 1: Prepare to complete the

GUIDED PRACTICE U 2 A 10 EXAMPLE 8 Step 1: Prepare to complete the square. Step 2: Move the constant to the side of the equation. Step 3: Calculate . Step 4: Add the calculation, to each side and simplify. ,

Step 5: Rewrite the trinomial as a binomial squared. Step 6: Move the constant

Step 5: Rewrite the trinomial as a binomial squared. Step 6: Move the constant back t the other side. The vertex form of the function is. The vertex is.

GUIDED PRACTICE U 2 A 10 EXAMPLE 9 Step 1: Prepare to complete the

GUIDED PRACTICE U 2 A 10 EXAMPLE 9 Step 1: Prepare to complete the square. Step 2: Move the constant to the side of the equation. Step 3: Factor out the leading coefficient from each term on th right hand side. Step 4: Calculate .

Step 5: Add the calculation, to each side and simplify. , Step 6: Rewrite

Step 5: Add the calculation, to each side and simplify. , Step 6: Rewrite the trinomial as a binomial squared. Step 7: Move the constant back t the other side. The vertex form of the function is. The vertex is.

GUIDED PRACTICE U 2 A 10 EXAMPLE 10 Step 1: Prepare to complete the

GUIDED PRACTICE U 2 A 10 EXAMPLE 10 Step 1: Prepare to complete the square. Step 2: Move the constant to the side of the equation. Step 3: Factor out the leading coefficient from each term on the right hand side. Step 4: Calculate .

Step 5: Add the calculation, to each side and simplify. , Step 6: Rewrite

Step 5: Add the calculation, to each side and simplify. , Step 6: Rewrite the trinomial as a binomial squared. Step 7: Move the constant back t the other side. The vertex form of the function is. The vertex is.

INDEPENDENT PRACTICE U 2 A 10 EXAMPLE 11

INDEPENDENT PRACTICE U 2 A 10 EXAMPLE 11

The vertex form of the function is. The vertex is.

The vertex form of the function is. The vertex is.

INDEPENDENT PRACTICE U 2 A 10 EXAMPLE 12

INDEPENDENT PRACTICE U 2 A 10 EXAMPLE 12

The vertex form of the function is. The vertex is.

The vertex form of the function is. The vertex is.

INDEPENDENT PRACTICE U 2 A 10 EXAMPLE 13

INDEPENDENT PRACTICE U 2 A 10 EXAMPLE 13

The vertex form of the function is The vertex is.

The vertex form of the function is The vertex is.

I can solve real-life problems using the technology, completing the square, factoring or the

I can solve real-life problems using the technology, completing the square, factoring or the square root method.

What is an extraneous solution?

What is an extraneous solution?

GUIDED PRACTICE U 2 A 10 EXAMPLE 14 An architect’s blueprints call for a

GUIDED PRACTICE U 2 A 10 EXAMPLE 14 An architect’s blueprints call for a dining room measuring 13 feet by 13 feet. The customer would like the dining room to be a square and not rectangular in shape and have an area of 250 square feet. How much will this add to he dimensions of the room?

GUIDED PRACTICE U 2 A 10 EXAMPLE 14

GUIDED PRACTICE U 2 A 10 EXAMPLE 14

GUIDED PRACTICE U 2 A 10 EXAMPLE 15 The area A in square feet

GUIDED PRACTICE U 2 A 10 EXAMPLE 15 The area A in square feet of a projected laser light show is given by , where d is the distance from the laser to the screen in feet. At what distance will the projected laser light show have an area of 100 square feet?

GUIDED PRACTICE U 2 A 10 EXAMPLE 15

GUIDED PRACTICE U 2 A 10 EXAMPLE 15

CHECK FOR UNDERSTANDING… Why can d not be negative?

CHECK FOR UNDERSTANDING… Why can d not be negative?

INDEPENDENT PRACTICE U 2 A 10 EXAMPLE 16 While designing a house, an architect

INDEPENDENT PRACTICE U 2 A 10 EXAMPLE 16 While designing a house, an architect used windows like the one shown to the right. What are the dimensions of the window if it has 2766 square inches of glass?

INDEPENDENT PRACTICE U 2 A 10 EXAMPLE 16 Hint: Find the area of the

INDEPENDENT PRACTICE U 2 A 10 EXAMPLE 16 Hint: Find the area of the rectangular window and the semicircular window.

INDEPENDENT PRACTICE U 2 A 10 EXAMPLE 16 Area of Rectangular Window: Area of

INDEPENDENT PRACTICE U 2 A 10 EXAMPLE 16 Area of Rectangular Window: Area of Semicircular Window:

INDEPENDENT PRACTICE U 2 A 10 EXAMPLE 16 Total Amount of Glass Used:

INDEPENDENT PRACTICE U 2 A 10 EXAMPLE 16 Total Amount of Glass Used:

INDEPENDENT PRACTICE U 2 A 10 EXAMPLE 16 Length cannot be negative. So the

INDEPENDENT PRACTICE U 2 A 10 EXAMPLE 16 Length cannot be negative. So the rectangular portion of the window is approximately 34 inches wide by 68 inches long. The semicircular top window has a radius of approximately