Week 1, Lesson 2 1. Warm up 2. Notes Quadratics 3. ICA Physics Rocket

Do all functions follow patterns? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 1, Lesson 2 1. Warm up 2. Notes Quadratics 3. ICA Physics Rocket Standard 6.3 11 Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up: Match the linear functions to their graphs f(x) = 2x 1 g(x) = x + 3 h(x) = 2x +2 1

Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Properties of Quadratics Quadratics 1. Any function that has a biggest exponent of 2 is called a quadratic 2. Any quadratic fits the form f(x) = ax 2 + bx + c (a cannot be 0) 3. All quadratics will always fit a "u" shape 4. All quadratic graphs are symmetrical Example 1 Use the t chart below to draw the graph of the quadratic given f(x) = x 2 4x + 2 x 0 1 2 3 4 f(x) Example 2 Use the t chart below to draw the graph of the quadratic given g(x) = (x 2) 2 + 2 x 0 1 2 3 4 f(x) Summary: 2

Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Quadratics Quadratics on a calc After graphing the quadratic, you can find x and y coordinates using G SOLVE Example 3 Use your calculator to complete the table below f(x) = 2x 2 4x + 6 x f(x) 3 2 1 0 1 Example 4 The number of Cardinals fans (y) is dependent on the number of games they have played (x). y = (x 9) 2 + 95000 a) How many fans did they have after 5 games? b) How many fans did they have after 9 games? a) How many fans did they have after 17 games? Summary: 3

Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity Physics Rocket Ms. Delp launches a model rocket with her physics class. They track the height (h) according to time (t) h(t) = 16t 2 + 120t t 0 1 2 3 4 5 6 7 8 h a) How high was the rocket after 3 seconds? b) When is the rocket at 75 feet? c) When does the rocket reach its peak? d) How high is the rocket at its peak? e) How long does it take the rocket to reach the ground again? 4

a Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra 5

How do you find the main point of a quadratic? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 1, Lesson 3 1. Warm up 2. Notes Min/Max 3. ICA Matching Standard 6.3 13 Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up: Use a t chart to graph the quadratic f(x) = (x 4) 2 + 2 x y 1 0 1 2 3 4 6

Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Min/Max Minimum Maximum The most important (x,y) point to find in a quadratic is the minimum or maximum maximum minimum Finding min/max When a quadratic is written in f(x) = ax 2 + bx + c you can find the x coordinate using the following formula: Then, plug x into the formula to find y Walk through Find the min/max of the function g(x) = x 2 4x 5 a b c g(2) = 2 2 4(2) 5 g(2) = 9 (2, 9) On a calc: Graph it Shift, G SOLV, min/max Summary: 7

Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Min/Max Minimum Maximum After finding the minimum or maximum, build the table around those points Pick a few points on the left side and a few points on the right side Example 1 Find the min/max of the quadratic, then graph it f(x) = 2x 2 8x + 2 x y Example 2 Find the min/max of the quadratic, then graph it f(x) = x 2 8x + 2 x y Summary: 8

vity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity Matching Minimums and Maximums Match the function with the vertex (max/min) and also the graph ( 5, 1) (1, 3) ( 2, 5) (3, 4) 9

Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra 10

WHAT IS THE ESSENTIAL QUESTION? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 1, Lesson 4 1. Warm up 2. Notes Domain 3. ICA Standards 6.1 & 6.3 15 Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up: Find the vertex of the function f(x) = 2x 2 + 8x 2 11

Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Domain Domain The set of values for which a function is defined The set of x values that ARE ALLOWED The set of x values that WORK and give an answer Written {x x } Pronounced "x such that x is " Domains of functions Write the domains of the functions drawn below {x x < 2 } {x x > 1 } {x x ε R } Domains of Quadratics Since you can plug any number into a quadratic, and since the graph of a quadratic extends forever, the domain of any quadratic function is x{x x ε R } Summary: 12

Attachments W2L1.docx Project Survey.docx Project Survey.xlsx Project Questionnaire.docx Project Questionnaire.xlsx