1. Without the use of your calculator, evaluate each of the following quadratic functions for the specified input values. (c) ( )

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1 Name: Date: QUADRATIC FUNCTION REVIEW FLUENCY Algebra II 1. Without the use of our calculator, evaluate each of the following quadratic functions for the specified input values. (a) g( x) g g ( 5) ( 3) x 9 (b) ( ) f x x + 8x f f ( 3) ( 1) (c) ( ) h x x x h h ( 0) ( ) + 6. Which of the following represents the -intercept of the graph of the quadratic function (Recall, that the -intercept of a graph alwas occurs when x 0.) (1) 7 (3) 7 () (4) For a particular quadratic function, the leading coefficient is negative and the function has a turning point 3, 14. Which of the following must be the range of this quadratic whose coordinates are ( ) (1) { 3} (3) { 14} () { 3} (4) { 14} 4. A parabola has one x-intercept of x and an axis of smmetr of x 4. Which of the following represents its other x-intercept (Hint, think of how far the given x-intercept is awa from the axis.) (1) x 3 (3) x 6 () x 10 (4) x 8 5. A quadratic function is shown in the table below. Which of the following statements is not true about the function based on this table Explain our choice. (1) The function has an x intercept of 3. () The function has a -intercept of 3. (3) The function s leading coefficient is negative. (4) The function has a turning point of ( 1, 4) x f ( x ) COMMON CORE ALGEBRA II, UNIT #6 QUADRATIC FUNCTIONS AND THEIR ALGEBRA LESSON #1 emathinstruction, RED HOOK, NY 1571, 015

2 6. Consider the quadratic function whose equation is ( ) (a) Sketch a graph of f on the grid provided. f x x + x 8. (b) Over what interval is f decreasing (c) Over what interval is f ( x ) < 0 x (d) State the range of f. APPLICATIONS 7. The number of meters above the ground, h, of a projectile fired at an initial velocit of 86 meters per second and at an initial height of 6. meters is given b h( t) 4.9t + 86t+ 6., where t represents the time, in seconds, since the projectile was fired. If the projectile hits its peak height at t seconds, which of the following is closest to its greatest height (1) 65 meters (3) 4 meters () 384 meters (4) 578 meters 8. Phsics students were modeling the height of a ball once it was dropped from the roof of a 5 stor building. The students found that the height in feet, h, of the ball above the ground as a function of the number of seconds, t, since it was dropped was given b h( t) t. From what height was the ball dropped To the nearest tenth of a second, determine the time at which the ball hits the ground. Provide evidence from a table to support our answer or solve this algebraicall if ou recall how to.

3 FLUENCY REFLECTING PARABOLAS 1. Which of the following equations would represent the graph of the parabola reflection in the x-axis (1) (3) x + x after a () (4) x + x The graph of 10 x represents the graph of x after (1) a vertical shift upwards of 10 units followed b a reflection in the x-axis. () a reflection in the x-axis followed b a vertical shift of 10 units upward. (3) a leftward shift of 10 units followed b a reflection in the -axis. (4) a reflection across the x-axis followed b a rightward shift of 10 units. 3. If f ( x) x + 5x 3 and g( x ) is the reflection of f ( ) of the following (1) g( x) x 5x 3 (3) ( ) g x x + 5x 3 () g( x) x + 5x+ 3 (4) ( ) g x x + 5x+ 3 x across the -axis, then an equation of g is which 4. If the point ( 3, 5) lies on the graph of a function ( ) graph of the function h( x) (1) ( 3, 5 ) (3) ( 5, 3) () ( 3, 5) (4) ( 3, 5) 5. If the function f ( x 4) the graph of f ( x) h x then which of the following points must lie on the were graphed, it would represent which of the following transformations to (1) A reflection in the x-axis followed b a rightward shift of 4 units. () A reflection in the -axis followed b a rightward shift of 4 units. (3) A reflection in the x-axis followed b a downward shift of 4 units. (4) A reflection in the -axis followed b a leftward shift of 4 units.

4 SHIFTING PARABOLAS AND TURNING POINTS 1. Which of the following equations would result from shifting x five units right and four units up (1) ( x 5) + 4 (3) ( x ) 4 5 () ( x+ 5) + 4 (4) ( x ) Which of the following represents the turning point of the parabola whose equation is ( ) (1) ( 3, 7) (3) ( 7, 3) () ( 3, 7) (4) ( 3, 7) 3. Which of the following quadratic functions would have a turning point at ( 6, ) (1) ( x+ 6) (3) ( x ) 5 6 () 3( x+ ) (4) ( x ) x Which of the following is the turning point of (1) ( 1, 4) (3) ( 6,104 ) () ( 6, 40) (4) ( 4,1) In vertex form, the parabola x 10x+ 8 would be written as [Hint: Use the table feature of our calculator] (1) ( x 5) 33 (3) ( x ) 10 9 () ( x 5) 17 (4) ( x ) 6. The turning point of the parabola is (1) (.5,1.75 ) (3) (.5, 8.5) () ( 5, 10.5) (4) (.5, 17.5)

5 Answers to Quadratic Function Review Homework 1. a. 16, 0 b. 6, -10 c. 6, 14. (4) 3. (3) 4. () 5. (3) 6. a. graph b. (, 1) c. 4 < x < d. 9 or 9, ) 7. () ft.; 4.3 sec. Answers to Reflecting Parabolas Homework 1. (4). () 3. (1) 4. () 5. (1) 6. (3) 7. (3) 8. a. f ( x) x 4x and graph f x x 4x and graph b. ( ) 9. (-5, -7) Answers to Shifting Parabolas and Turning Points Homework 1. (1). (4) 3. (3) 4. () 5. () 6. (3)