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Algebra II – Problem Set Name:____________________ Unit 3 Quadratic Functions Block:______________ 1) For each of the following, write the form of the equation for the quadratic function and then explain how to graph the function from that particular equation. a) Standard Form:_____________________________________ b) Vertex Form:_______________________________________ c) Intercept Form:______________________________________ 2) Graph each of the following and label the vertex, axis of symmetry, and zeros. 1 2 a ) f ( x) 2 x 3 5 c) y x 4 x 2 b) g ( x) 2 x 2 6 x 5 2 3) Factor each of the following completely. a) x 2 8x 16 b) 7 x 2 11x 6 d ) 9 x 2 12 x 4 e) 81a 2 25 c) 5x 2 11x 12 f ) x 2 29 x 54 4) Write the function in vertex form. Then, identify the vertex and axis of symmetry. f ( x) x 2 12 x 20 5) Write the function in standard form. f ( x) 2 x 3 5 2 6) Find the discriminant and determine the nature of the roots for the function g ( x) 4 x 2 3x 2 . 7) Select all of the following that have two distinct real roots: a) y 6 x 2 2 x 3 b) f ( x) 9 x 2 3x 2 c) g ( x) 2 x 2 8x 8 d) h( x) 5x 2 x 4 e) y x 2 6 x 9 f) k ( x) 4 x 2 4 x 5 8) Write the equation of each graph shown in both intercept and vertex forms. a) b) 9) Select all of the following functions which have no real solutions. A) B) C) D) E) F) 10) Give an example of a real-world situation that is modeled by a quadratic function. 11) Describe the transformation of the equation f ( x) x 5 3 compared to its parent function 2 f ( x) x 2 . 12) Write the equation given graphical transformations of a downward shift of 1, a right shift of 6 and a stretch (narrow) of 2. 2 13) GRAPH: y= -x - 6x - 5 What is the vertex?________________________ What is the y-intercept?:_______________ What is the axis of symmetry? _______________ What is the domain?_______________________ What is the range?:_________________________ What is the max or minimum point? ___________________ How many roots are there?________________ What are the solutions of this equation? __________________ What do you call these solutions? _____________________ Where is the graph increasing?:_______________________ Where is the graph decreasing?:_______________________