Algebra 1. 7 th Standard Complete Graphs. Categories Quadratic (p. 3-9) Exponential (p ) Absolute Value (p ) Linear (p.
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1 Algebra 1 7 th Standard Complete Graphs Categories Quadratic (p. -9) Eponential (p. 10-1) Absolute Value (p ) Linear (p. 18-9) Summative Assessment Date: Wednesda, November 8 th Page 1
2 Standard: Complete Graphs Learning Targets Linear Graphs Learning Target I can completel graph a linear function in standard form b finding the intercepts from the equation. I can completel graph a linear function in slope-intercept form. I can completel graph a linear function in point-slope form. I can completel graph a horizontal and vertical line. Quadratic Graphs Learning Target I can determine if the graph opens up or down. I can find the verte of a quadratic function in standard form. I can completel graph a quadratic function in standard form. I can find the verte of a quadratic function in verte form. I can completel graph a quadratic function in verte form. Absolute Value Graphs Learning Target I can determine if the graph opens up or down. I can find the verte of an absolute value graph. I can determine the slope of each side of the absolute value graph. I can completel graph an absolute value function. Eponential Graphs Learning Target I can find the boundar line (min/ma line) of the eponential function. I can find at least one ke point from the equation. I can completel graph an eponential function. How did I do on the HW? How did I do on the HW? How did I do on the HW? How did I do on the HW? How did I do on the class check? How did I do on the class check? How did I do on the class check? How did I do on the class check? Do I need to practice more? Do I need to practice more? Do I need to practice more? Do I need to practice more? Page
3 Complete Graphs DAY 1 Notes Quadratic Eample 1: Analze the graph of the function = + 4b answering the following questions. A. Does the graph open up or down? B. What is the maimum/minimum? C. Is there a vertical shift from the parent function? D. Is there a horizontal shift from the parent function? E. What is the verte? F. What is the leading coefficient (the a value)? *Tip You can use the leading coefficient (the a value) to get two more points on the graph quickl. Now plug a few more values in the equation to get points to complete the graph. Eample : Analze the graph of the function ( ) = 6b answering the following questions. A. Does the graph open up or down? B. What is the maimum/minimum? C. Is there a vertical shift from the parent function? D. Is there a horizontal shift from the parent function? E. What is the verte? F. What is the leading coefficient (the a value)? Now plug a few more values in the equation to get points to complete the graph. Page
4 = Eample : Analze the graph of the function ( ) A. Does the graph open up or down? B. What is the maimum/minimum? C. Is there a vertical shift from the parent function? D. Is there a horizontal shift from the parent function? E. What is the verte? F. What is the leading coefficient (the a value)? Now plug a few more values in the equation to get points to complete the graph. To Graph ALL Quadratic Functions You MUST have the. Find this first! Strateg #1: Determine if the graph or. Strateg #: Use the to find two more points on graph. Strateg #: Use a to get more points to complete the graph. Find the verte of each of the following functions. A. = B. = + 7 C. ( ) = D. = ( + ) 16 E. 0.5( ) = F. = Page 4
5 Eample 4: = 8 + What is different? This equation is in Standard Form, which looks like = a + b + c. To graph this equation, we still must follow the steps from before. To find the Verte, we use the b following formula for the -coordinate: =. a Plug this value into the original equation to find the -coordinate of the verte. A. What is the verte? B. Does the graph open up or down? C. What is the leading coefficient (the a value)? Now plug a few more values in the equation to get points to complete the graph. Eample 5: Graph the function = + 1 Eample 6: Find the verte of the function = + 6 Page 5
6 Tr these with a partner 1. Graph = 6 1 A. What is the -intercept? B. What are the -intercepts approimatel? C. What is the min/ma? D. Describe an transformations FROM the parent function =. Graph = A. What is the min/ma? B. What are the -intercepts? C. Describe an transformations FROM the parent function = Page 6
7 Complete Graphs DAY 1 Homework Quadratic Graphs For #1-6, find the verte, determine if the graph opens up or down, and identif the leading coefficient. 1. = 5. ( 1) = +. ( ) = Verte Verte Verte Opens Opens Opens Lead. Coeff. Lead. Coeff. Lead. Coeff. 4. = = = Verte Verte Verte Opens Opens Opens Lead. Coeff. Lead. Coeff. Lead. Coeff. For the remaining problems, graph each function = Page 7
8 = + 8. ( ) 9. ( ) = = Page 8
9 11. = 5 1. = = + 6 Page 9
10 Complete Graphs DAY Notes Eponential Asmptote As we continue in the negative direction, what do ou notice about the graph? It starts to look like a horizontal line. The -value of this horizontal line is. This is called the asmptote, it is the number that the eponential function approaches. It is the ma or min of an eponential function. ( ) Eponential graph: = a( b) h + k THE NUMBER YOU ADD AT THE END (MAX OR MIN) IS THE ASYMPTOTE Graphing an equation Things to know: 1. asmptote (remember, this is the min or ma). If it has a min or a ma. Open up or open down 4. -intercept 5. You can plot a few points for a more eact graph. EX 1 Page 10
11 EX EX EX 4 Page 11
12 Complete Graphs DAY Homework Eponential #1 : Create a graph for the following equations Page 1
13 #4 7: Graph the following functions 4. = = = = Page 1
14 Complete Graphs DAY Notes Absolute Value Use each absolute value graph, state whether it opens up or down, what the verte is and find the slope of each side. = Opens : Verte: Slopes/ Rate of Change: = Opens : Verte: Slopes/ Rate of Change: 1 = + Opens : Verte: Slopes/ Rate of Change: Page 14
15 Graphing Absolute Value Functions Graph each of the following Absolute Value Functions. EX 1: = + 1 EX : = Opens : Verte: Slopes/ Rate of Change: Opens : Verte: Slopes/ Rate of Change: EX : 1 = + 1 Page 15
16 Complete Graphs DAY HW Absolute Value #1-: Use each absolute value graph, state whether it opens up or down, what the verte is and find the slope of each side. 1. = +. 5 = = Opens : Opens : Opens : Verte: Verte: Verte: Slopes/ Rate of Change: Slopes/ Rate of Change: Slopes/ Rate of Change: #4-9: Graph each absolute value function. 4. = = = 1 7. = 4 Page 16
17 8. = + 9. = #10-11: Give the equation of the graph shown Equation: Equation: Page 17
18 Complete Graphs DAY 4 Notes Linear Functions (Slope-Intercept & Point-Slope) Slope-Intercept Form Review: = + This is a equation. What information does this equation show? When a linear equation is in this form, it's called Slope-Intercept Form where, Graph: = + All we need to know is: m = b = Graph: = 5 All we need to know is: m = b = Page 18
19 Graph: 1 = 4 All we need to know is: m = b = Graph: = + 1 All we need to know is: m = b = Point-Slope Form Let s look at this equation: = ( ) 5 This is a equation. What information does this equation show? When a linear equation is in this form, it's called Point-Slope Form where, Page 19
20 Graph: = ( ) 5 All we need to know is: m = Point: Graph: = ( + 4) + 1 All we need to know is: m = Point: Graph: = ( + ) 4 All we need to know is: m = Point: Page 0
21 Graph: = ( 5) + All we need to know is: m = Point: Graph: 1 = ( + ) + 6 All we need to know is: m = Point: Graph: = ( + ) 4 All we need to know is: m = Point: Page 1
22 Complete Graphs DAY 4 HW Linear Functions (Slope-Intercept & Point-Slope) 1. Graph the equation: 6 =. Graph the equation: = + 7 m = b = m = b =. Graph the equation: = Graph the equation: 1 = + 5 m = b = m = b = Page
23 5. Graph the equation: = 9 6. Graph the equation: 4 = 6 5 m = b = m = b = 7. Graph the equation: = ( ) Graph the equation: = ( ) 6 m = Point: m = Point: Page
24 9. Graph the equation: = 4( + 5) Graph the equation: 1 = ( 6) 1 m = Point: m = Point: 11. Graph the equation: = ( + 1) 8 5 = ( + 7) 1. Graph the equation: m = Point: m = Point: Page 4
25 Complete Graphs DAY 5 Notes Linear Functions (Standard Form) What Linear Forms have ou know? STANDARD FORM: 1) Graph + = 18. Step1: intercept Step: intercept Step: Plot and Graph ) Graph = 6. Step1: intercept Step: intercept Step: Plot and Graph Page 5
26 YOU TRY: A) 4 = 8 B) 5 = 0 How to graph lines that are missing a variable: A) B) C) D) SUMMARY: ** Slope-Intercept Form ** Point-Slope Form **Standard Form **Steps to graphing Standard Form: 1) ) ) ** Equations like = # are **Equations like = # are Page 6
27 Complete Graphs DAY 5 HW Linear Functions (Standard Form) Find the and intercepts for each equations. REMEMBER, all answers would be written as points: (, ) = = intercept: -intercept: -intercept: -intercept: -intercept: -intercept: 4. = 6 5. = 6. = 5 -intercept: -intercept: -intercept: -intercept: -intercept: -intercept: = = 6 9. = 15 -intercept: -intercept: -intercept: -intercept: -intercept: -intercept: Page 7
28 Graph each equation = = = = = = 18 Page 8
29 Graph each line using an method ou know. 16. = f ( ) = ( 1) = f ( ) = 9 0. = 1. =. 4 + = = = 18 4 Page 9
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