6.4 6.notebook December 03, 2018
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1 6.4 Opening Activity: 1. Expand and Simplify 3. Expand and Simplify (x 5) 2 y = (x 5) Expand and Simplify 4. Expand and Simplify (x 5) 2 3 y + 3 = (x 5) 2 5. What is the vertex of the following equations? a. y + 3 = (x 5) 2 b. y = x 2 10x +22
2 Graphing y = ax 2 + bx + c Objectives: Graph equations in standard form Convert equations from vertex form to standard form Find critical information on a graph (vertex, y intercept, opens up/down, wide/narrow)
3 6.4 Activity 1: Using your graphing calculator (or Desmos), graph the following equations. Write your responses to the questions on the white paper in your bin. First Equation: y + 1 = 2(x 3) 2 Second Equation: y + 1 = 2(x 3) 2
4 Activity 1: What is the irst equation you were asked to graph? What is the second equation you were asked to graph? How are the two equations alike? How are the two graphs alike? How are the two graphs different? How are the two equations different?
5 6.4 Activity 2: Using your graphing calculator (or Desmos), graph the following equations. Write your responses to the questions on the white paper in your bin. First Equation: y + 1 = 2(x 3) 2 Second Equation: y + 1 = 0.5(x 3) 2
6 Activity 2: What is the irst equation you were asked to graph? What is the second equation you were asked to graph? How are the two equations alike? How are the two graphs alike? How are the two graphs different? How are the two equations different?
7
8 6.4 Activity 3: Graph the following equation: y + 1 = 2(x 3) 2 Write the equation in standard form (expand and simplify) Graph your answer to make sure it's the same equation.
9 Activity 3: How does the graph of each equation tell you that they are equivalent expressions? What is the y intercept of the graph? Which equation contains that number? What is the vertex of the graph? Which equation contains both of those numbers?
10 6.4 Vertical Motion Model: In physics, an object in free fall will change in position utilizing the following equation: h = 16t 2 + vt + s h the dependent variable; height. t the independent variable; time. v = the starting velocity of the object (if it is just dropped, then it will be zero. s = the starting height of the object. *The 16 represents the acceleration due to gravity in ft/s 2. If an egg is flung upward with an initial velocity of 80 ft/s from a starting height of 5 ft, how high in the air is the egg after 2 seconds? How high in the air is the egg after 8 seconds?
11 6.5 Activity 4: Complete the activity on the white paper in your bin. For all four problems, what is the relationship between the value of b and the value of c?
12 Activity 4: Expanding Binomials Activity Expand each binomial and write in ax 2 + bx +c form (x 4) 2 a = b = c = 2. (x + 12) 2 a = b = c = 3. (x 8) 2 a = b = c = 4. (x + 5) 2 a = b = c =
13 Completing the square to make a perfect square trinomial. To make a perfect square trinomial out of ax 2 + bx you must add to the expression.
14 6.5 Use the results of Activity 4 to find the number that completes the square in each quadratic expression below. x 2 + 2x +? x 2 + 6x +? x 2 8x +?
15 6.6 Opening Activity: Using your graphing calculator, or algebra skills, fill in the table below for the following equation. y 5 = (x + 1) 2 x y
16 Fitting a quadratic model to data Objectives: Explore the characteristics of data that is best represented with a quadratic model. Fit a model to a given set of data. Make predictions about a situation using a quadratic model.
17 6.6 Make a table of values from x = 3 to x = 3 for the following equations. y = 3x + 1 x y y = 3x x y What is the pattern in the y values for each table?
18 6.6 Given the table below, do to points form a line or a parabola? x y What is an equation for this set of points?
19 6.6 x y *Same table from the last page. What is the y intercept of this set of data? What is the vertex of this set of data? Does the graph open up or down?
20 6.6 Given the table below, what will y equal when x = 12? x y What will x be when y = 575?
21
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Prerequisite Skills This lesson requires the use of the following skills: simplifying radicals working with complex numbers Introduction You can determine how far a ladder will extend from the base of
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Fast Five Lesson 19 Factoring Polynomials Factor the number 38,754 (NO CALCULATOR) Divide 72,765 by 38 (NO CALCULATOR) Math 2 Honors - Santowski How would you know if 145 was a factor of 14,436,705? What
Modeling with quadratic functions Student Activity Sheet 5; use with Exploring Using y = ax 2 + bx + c to model data
1 What relationship is being compared when discussing Pete s shot? Horizontal distance in feet, x Height in feet, y 0 30 60 90 120 150 65 80 90 98 102 100 2 Use a graphing calculator to make a scatterplot