KEY Algebra: Unit 9 Quadratic Functions and Relations Class Notes 10-1
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1 Name: KEY Date: Algebra: Unit 9 Quadratic Functions and Relations Class Notes 10-1 Anatomy of a parabola: 1. Use the graph of y 6 5shown below to identify each of the following: y 4 identify each of the following:. Use the graph of shown below to a) Ais of symmetry 3 b) Roots 1, 5 c) Verte 3, 4 d) Turning Point 3, 4 e) Solutions 1, 5 a) Ais of symmetry 0 b) Roots, c) Verte 0,4 d) Turning Point 0,4 e) Solutions,
2 3. Graph y 3. Use your calculator to fill in the table, then plot your coordinates. (You may need to scroll in the table to find coordinates to plot.) What is the equation of the ais of symmetry? 1.5 y What are the roots? 3, 0 Roots are where the parabola crosses the ais. 3. Graph y 3 Use your calculator to fill in the table, then plot your coordinates. y What is the equation of the ais of symmetry? 1.5 What are the roots? 3, 0 Roots are where the parabola crosses the ais. 4. Is the coordinate 0,7 on the graph of y 8 7? Eplain your answer. Yes, when you plug a 0 in for, and simplify, the y-value is What is the ais of symmetry of the parabola y 10 4? 5
3 Name: KEY Date: Algebra: Unit 9 Quadratic Functions and Relations Class Notes Using the graph on the right, answer each of the following: What is the equation of the ais of symmetry? 3 What is the turning point? 3, 4 What are the roots? 1, 5 What is the equation of the parabola? The roots are and - and come from the factors ( + ) and ( ) y 6 5 For each of the following quadratics: a) Graph the equation on the graph provided. b) State the solutions/ roots. c) State the equation of the ais of symmetry. d) State the coordinates of verte.. y 6 y a. Verte/ Turning Point 0.5, 6.5 b. Ais of Symmetry 0.5 c. Roots, 3
4 3. y 6 y d. Verte/ Turning Point 3,9 e. Ais of Symmetry 3 f. Roots 0, 6 4. y 15 a. Verte/ Turning Point 1,16 y b. Ais of Symmetry 1 c. Roots 3, 5 5. What is the ais of symmetry of the parabola represented by y 6 4? 3 6. What is the turning point of the parabola represented by y 6 4? 3,5
5 Name: KEY Date: Algebra: Unit 9 Quadratic Functions and Relations Class Notes 10-3 In 1-4, solve the quadratic equations y y 7. y 4 8. y 10 7
6 9. What are the roots of questions #5-8? #5. = -3, = 3 #6. = -1, = #7. = 0, = 4 #8. = -5, = What are the solutions to #1-4? #1. = -3, = 3 #. = -1, = #3. = 0, = 4 #4. = -5, = Are there any similarities between the solutions to #1 and the roots of #5? They are eactly the same. 1. Do the similarities eist for questions #-4 and #6-8? They are eactly the same. Use the graphs below to answer questions a. What are the roots of the quadratic? 1, 7 b. What are the factors that would correlate with the roots? 1 7 c. What is the equation of the parabola? y b. What is the turning point? 4, 9 4 c. What is the ais of symmetry? 14. a. What are the roots of the quadratic?, b. What are the factors that would correlate with the roots? c. What is the equation of the parabola? y 0, b. What is the turning point? c. What is the ais of symmetry? 0
7 Name: KEY Date: Algebra: Unit 9 Quadratic Functions and Relations Class Notes What are the verte and ais of symmetry of the parabola y 16 63? Verte is8, 17, the ais of symmetry is 8. The equation y 8is graphed on the set of aes below. Based on this graph, what are the roots of the equation 8 0? The roots are where a parabola crosses the -ais. 4, 3. Use the graph below to answer each of the following. a. What are the solutions to the system of equations? ( 3,5) and 1, 3 b. What are the roots of the quadratic function?, c. What factors would the roots from (b) produce?, d. What is the equation of the quadratic function? y 4 4 e. What is the equation of the line? Slope = -, y-intercept = (0, -1) y 1
8 4. On the set of aes below, solve the following system of equations graphically and state the coordinates of all points in the solution set. y 4 y 1 1,3 and 3, 5 b. Check your answers algebraically. (Plug them into BOTH equations) Check 3, EQ # EQ # 3 1 Check 3 1 3, EQ # EQ #5 y On the set of aes below, solve the following system of equations graphically and state the coordinates of all points in the solution set. 4 9 y1,5 and 4,9 b. Check your answers algebraically. Check, 5 EQ # EQ # 5 1 Check 4, EQ # EQ #
9 Name: KEY Date: Algebra: Unit 9 Quadratic Functions and Relations Class Notes Use the graph on the right to answer each of the following questions. a. What is the ais of symmetry? b. What is the turning point?, 8 c. What are the roots/ solutions? 5, 1 d. What is the equation of the quadratic? 5, y e. Plug the equation from (d) into your calculator, and graph it. Do the coordinates in the table match the graph?. Graph y below, and use it as your baseline graph for questions Graph y. How does it compare to the original? Moved 3 units to the RIGHT. 4. Graph y. How does it compare to the original? Moved units to the LEFT Predict what y will look like and use your calculator to check your prediction. Moved 1 unit to the RIGHT. 6. Graph y 4. How does it compare to the original. Moved DOWN 4 units. 7. Graph. How does it compare to the original? y 4 Moved UP 4 units. 8. Predict what y1 will look like, and use your calculator to check your prediction. Moved 1 units to the RIGHT. 9. Write a rule that describes how a parabola is moved when numbers are added or subtracted.addition or subtraction outside of the parenthesis move the parabola up(+) or down(-). Addition or subtraction outside of the parenthesis move the parabola left (add) or right(subtract).
10 10. Use your calculator to graph y on the aes below. Keystrokes to graph absolute value functions: 1. Press Y=. Press MATH, Right Arrow, then select abs( 3. Press ENTER, abs( should be copy and pasted into Y=) 4. Press GRAPH y 11. Graph y 1. Graph y Are the conclusions you made in questions 5-7 valid for absolute value graphs? Eplain. Yes,Addition or subtraction outside of the parenthesis move the parabola up(+) or down(-). Addition or subtraction outside of the parenthesis move the parabola left (add) or right(subtract).
11 Name: KEY Date: Algebra: Unit 9 Quadratic Functions and Relations Class Notes Which ordered pair is a solution to the system of equations y and [A], [B] 0,0 [C] 1,1 [D],. What are the verte and ais of symmetry of the parabola y 16 63? [A] Verte: 8, 17 ; ais of symmetry: = 8. [B] Verte: 8,17 ; ais of symmetry: = 8. [C] Verte: 8, 17 ; ais of symmetry: = -8. [D] Verte: 8,17 ;ais of symmetry: = -8. y? 3. Which equation represents the ais of symmetry of the graph of the parabola below? Plug the coordinates into each the equation. It must work for BOTH coordinates. Equation of ais of symmetry is: b 16 8 a 1 To find the y value of the verte, plug 8 in to the equation. 8, 17 ` Graphically, the ais of symmetry is the equation of the vertical line that goes through the verte/ turning point. 3 [A] 3 [B] 5 [C] y 3 [D] y 5 4. The height, y, of a ball tossed into the air can be represented by the equation, y 10 3 where is the elapsed time. What is the equation of the ais of symmetry of this parabola? [A] y 5 [B] 5 [C] y 5 [D] 5 5. The solution set of the equation 41 0is: b 10 5 a 1
12 6. Graph y 7. Graph y 3 8. Graph y 9. Graph y 10. What effect does a negative in front of the absolute value have? Yes, addition or subtraction outside of the parenthesis move the absolute value graph up(+) or down(-). Addition or subtraction outside of the parenthesis move the absolute value graph left (add) or right(subtract). 11. What effect does multiplying by inside the absolute value have? Multiplying by inside the parenthesis make the function grow twice as fast, making it steeper.
13 Name: KEY Date: Algebra: Unit 9 Quadratic Functions and Relations Class Notes A swim team member performs a dive from a 14-foot-high springboard. The parabola below shows the path of her dive. Graphically, the ais of symmetry is the equation of the vertical line that goes through the verte/ turning point. 3 Which equation represents the ais of symmetry? [A] 3 [B] 3 [C] y 3 [D] y 3. Graph and label the following equations on the set of aes below. y 1 y Eplain how decreasing the coefficient of affects the graph of the equation. As the coefficient of decreases, the graph of the absolute value equation gets wider.
14 6. Graph y 7. Graph y 3 8. Graph 1 y y 9. Graph 7. Why does the graph of y 1 look different than the other 3? One raised to any power is 1, thus the graph of y 1 is the same as y 1.
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