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Unit 2 Transformation of a Parent Function & Quadratics Assessment Name: _________________________________ Date: _______ Period: ________ 2.1 Transformation of a Parent Function #1-4 /15 /100 2.2 Completing the Square # 5-6 /10 /100 2.3 Modeling with Quadratics #7-8 / 10 /100 1. a) Make a graph of a Square Root function with the locator point at (4, 2), and with two other coordinates (5, 4) and (8,6). (4 points) b) Write the equation in graphing (vertex) form. Y = 2 times square root of (x – 4) + 2 change to vertex form 2. Consider the graph of y = (x + 5)2 + 1 Make one change in the original equation of f (x) so that the graph: (6 points) a. Opens downward. b. Is fatter (compressed). c. Has x-intercepts. d. Is moved to the left. e. Has an "S" shape. f. Has a “V” shape 3/12/2016 1 Unit 2 Transformation of a Parent Function & Quadratics Assessment Name: _________________________________ 3. What are the asymptotes of 𝑓(𝑥) = 1 𝑥−3 Date: _______ Period: ________ + 2(1 point) 4. Explain how the following function, in graphing form has been transformed compared to the original parent function y = x3. (4 points) y = -.5(x +4)3 - 2 -----------------------------------------------------------------Finished to here ---------------------------------5. Use the complete the square process to rewrite the quadratic in vertex form, then identify the vertex: (3 pts each) a. 𝑦 = 𝑥 2 + 6𝑥 − 2 b. 𝑦 = 𝑥 2 + 7𝑥 + 20 3/12/2016 2 Algebra 2 Unit 2 Pre-Test Review Worksheet Vertex Form: Vertex Form: Vertex: Vertex: 6. Use the complete the square process to rewrite the equation in graphing form of a circle: (4 pts) 𝑥 2 + 𝑦 2 − 4𝑥 + 6𝑦 − 3 = 0 Equation: Center: ( , ) Radius: 7. When Twinkle Toes Tony kicked a football, it landed 150 feet from where he kicked it. It also reached a height of 130 feet. Write an equation that, when graphed, will model the path of the ball from the moment it was kicked until it first touched the ground. Also sketch the path of the ball and label the key points. Show all work. (5 points) 3/12/2016 3 Algebra 2 Unit 2 Pre-Test Review Worksheet 8. At a recent egg-tossing contest, one student threw an egg that left his hand 3 feet off the ground and landed 80 feet away in his partners hand which was also 3 feet off the ground. Someone in the crowd observed that the egg reached a maximum height of 16 feet off the ground. Draw a diagram to model the path the egg traveled and label the key points. What equation could be used to model the path of the tossed egg? (5 points) 3/12/2016 4