Algebra II Honors Unit 3 Assessment Review Quadratic Functions. Formula Box. f ( x) 2 x 3 25 from the parent graph of

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1 Name: Algebra II Honors Unit 3 Assessment Review Quadratic Functions Date: Formula Box x = b a x = b ± b 4ac a h 6t h 0 ) What are the solutions of x 3 5? x 8or x ) Describe the transformation of f ( x) x 3 5 from the parent graph of Right 3 units, down 5 units, vertical stretch, reflected graph 3) Find the zeros of x x 0 3 y x x x 0 or x 3 0 x or x g( x) x. 4) This year s AP Statistics classes conducted an experiment to determine the number of hours of study that led to the highest score on their mid-term exam. They found that the exam score, S, for each student who studied x hours can be modeled by S ( x) 0.853x 7.48x Find the maximum score obtained on the exam. How many hours of studying maximizes the vertex 0.3,96.5 The maximum score obtained on the test was a To exam score? maintain this score you must study for about 0.3 hours. 5) Given the graph, identify the a. Roots of the function 3,0,,0 b. Maximum or minimum value y 4 c. Domain,, d. Range y/ y 4, 4,

2 Height (feet) 6) Determine the discriminant of the following quadratic equations. How many real solutions does each equation have? a. x 0x 3 0 b. x 0x 5 0 c. x 0x 7 0 b 4ac Two real solutions 7) Solve each equation by factoring. a. b 4ac One real solution x 5x4 0 b. x x 0 x 7 x 0 x 4 x 3 0 x 7 0 or x 0 c. x 7 or x x 0 or x 3 0 x or x 3 x 4 0 or x 3 0 x 4or x 3 3x 0x 7 0 x 9x 36 0 d. x x x x 3x 0 or x 7 0 x or x 7 3 b 4ac No real solution 8) My sister is so annoying, that I decided to put her in a rocket and launch her into space (just kidding. I made a doll that looked like her and launched that into the air. It didn t go very far). The rocket was launched from ground level vertically into the air with an initial velocity of 80 ft per second. The height of the rocket, h(t) after t seconds is given by ht 6 t( t 5). a. Graph the function. Label both axes and state an appropriate scale. b. When will the rocket reach its highest point? The rocket reaches its highest point in about.5 seconds. What is the maximum height of the rocket? The maximum height of the rocket is about 00 feet in the air. c. How long with the rocket stay in the air? The rocket is in the air for about 5 seconds. Time (seconds)

3 9) A volleyball is dropped from the top of the gym bleachers at a height of 40 feet above the gym floor. Write a quadratic function to model the volleyball s height h (in feet above the ground) after t seconds. h 6t 40 0) A volleyball is hit upward by a player in a game. The height h (in feet) of the volleyball after t seconds is given by the function h 6t 30t 6. After how many seconds will the volleyball hit the ground? 0 6t 30t 6 a 6, b 30, c t t 3 t 0.8 or t.06 f ( x) x 8 3 ) Given the function The volleyball will hit the ground in about. seconds. a) State a, h, and k. a =, h = 8, k = 3 b) The graph opens down. c) Describe the horizontal and vertical translation represented by this function. The graph is shifted 8 units left and 3 units down d) Does the function contain a vertical stretch or shrink when compared to the parent graph? Vertical stretch f) Identify the domain.,, i) Re-write f(x) in standard form. y x 8 x 8 3 y x x x y x x y x x y x x g) Identify the range. y/ y 3,, 3 h) Graph the function. 3 3

4 vertex ) Write the equation of the parabola in vertex form. 3, 6 point on curve, y a x h k a 3 6 4a 4 4a a y x ) Given the function f ( x) x 4x 5 a) State a, b, and c. a =, b = 4, c = 5 b) Identify the axis of symmetry. b 4 x a c) Determine the vertex. d) y-intercept 0, 5 e) x-intercepts 5,0,,0 f) Rewrite f(x) in intercept form f x x x f x x x g) Identify the range. y/ y 9, 9, h) Graph the function. f vertex, 9

5 4) The area of a triangle is 3 cm. The height of the triangle is 4x and the base of the triangle is x + 6. Draw a picture of the triangle and label the base and height. What is the value of x? What are the dimensions of the length of the base and the height of the triangle? 4x x+6 l w A 4 x x x x x 3x3 x 6 x _ 64 _ 6 _ 64 _ x 8 5 x 8 5 x 8 5 The value of x = 7 cm. The height of the triangle is 8 cm and the base of the triangle is 3 cm. 5) Two pennies are launched from the top of the Empire State Building, which is 50 feet high (excluding the lightening rod). a) The first penny is launched upward with an initial velocity of feet per second. How long will it take for the penny to hit the ground? (Remember h = 6t + v 0 t + h 0 ) b) The second penny is launched downward with an initial velocity of feet per second. How long will it take for the penny to hit the ground? (Remember h = 6t + v 0 t + h 0 ) h 50 ft, v ft / sec, h 0, t? t t t 8044 t 3 t 8.47sec. or t 9. sec. h 50 ft, v ft / sec, h 0, t? t t t 8044 t 3 t 9.sec. or t 8.47 sec. c) Write a height model if one of the pennies is dropped from the building. h 6t 50

6 6) Write the equation for each of the following parabolas. Put your final answer in vertex form. a) b) y a x h k 0 a a a 4 a y a x h k 3 a 0 3 a 3 4a 4 4a a c) d) a a y a x p x q a 3 a y 3 x x graph and find vertex to be, 4 x y Not enough information to answer question

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