Algebra 2B CH 5. WYNTK & TEST Algebra 2B What You Need to Know , Test

Transcription

1 Algebra 2B CH 5 NAME: WYNTK & TEST DATE: HOUR: Algebra 2B What You Need to Know , Test A Be able to use transformations to graph quadratic functions and answer questions. Using the graph of f(x) = x 2 as a guide, describe the transformations, and then graph each function. Identify the vertex, find the domain and range, and the zeros of the functions 1. g(x) = (x 3) g(x) = (x + 2) 2 1 Vertex: (, ) D:{ } R: { } Vertex: (, ) D:{ }R:{ } Zeros: (, ) (, ) Zeros: (, ) (, ) 3. g(x) = (x) g(x) = - 2(x) 2 Vertex: (, ) D:{ } R: { } Zeros: (, ) (, ) Vertex: (, ) D:{ }R:{ } Zeros: (, ) (, )

2 A Be able to use transformation descriptions to write quadratic function in vertex form y = a(x h) 2 + k. Use the description to write each quadratic function in vertex form. 5. f(x) = x 2 is vertically stretched by a factor of 5 and translated 2 units left to create g(x). 6. f(x) = x 2 is reflected across the x-axis, vertically compressed by ⅓ and translated 4 units down to create g(x). 7. f(x) = x 2 is reflected across the x-axis and translated 4 units up to create g(x). 8. f(x) = x 2 is reflected across the x-axis and translated 6 units right to create g(x). A , A & A From it s standard form equation, be able to determine if the graph opens up or down, find the axis of symmetry, vertex and Min/Max value 9. The highway mileage m in miles per gallon for a compact car is approximated by m (s) = 0.025s s 30, where s is the speed in miles per hour. What is the maximum mileage for this compact car to the nearest tenth of a mile per gallon? What speed results in this mileage? a) Determine whether the graph opens up or down b) Find the axis of symmetry c) Find the vertex d) Find the Minimum/Maximum mileage for this compact car? e) What speed results in this mileage? 10. The power p in horsepower, hp generated by a high-performance speedboat engine operating at r revolutions per minute, rpm can be modeled by the function p(r) = r r What is the maximum power of this engine to the nearest horsepower? At how many revolutions per minute must the engine be operating to achieve this power? a) Determine whether the graph opens up or down b) Find the axis of symmetry c) Find the vertex d) Find the Minimum/Maximum power of this engine to the nearest horsepower. e) How many revolutions per minute must the engine be operating to achieve this power A Be able to use a graph and table to find zeros of a quadratic function. Graph each function in your graphing calculator. Then using a graph and a table from your graphing calculator find the zeros of the function. 11. f(x) = 12. f(x) = A Be able to find zeros by factoring, ac method, square roots, GCF

3 Find the zeros of the quadratic functions by factoring A Be able to find Max/Min height of an object using a quadratic model. 18. The height h of an arrow in feet is modeled by h (t) = - 16t t + 4, where t is the time in seconds since the arrow was shot. How long is the arrow in the air before it hits the ground? a) When the height of the arrow = the arrow is on the ground. b) Factor to find the values of time, t when the arrow is on the ground. 19. A bald eagle snatches a fish from a lake and flies to an altitude of 256 ft. The fish manages to squirm free and falls back down into the lake. Its height h in feet can be modeled by h (t) = t 2, where t is the time in seconds. How many seconds will the fish fall before hitting the water? a) When the height of the fish = the fish hits the water. b) Factor to find the values of time, t when the fish hits the water. 20. A rocket is launched from ground level vertically into the air. The height of the rocket, h(t), after t seconds is given by h(t) = - 16t t. How high can you expect the rocket to go and how long it will be in the air? a) When the height of the rocket = the fish hits the water. b) Factor to find the values of time, t when the fish hits the water.

4 A Be able to graph quadratic inequalities Graph the following quadratic inequalities, determine it the parabola opens up or down, find the axis of symmetry, vertex, Min/Max value, and y-intercept. Determine if the boundary line is solid or dashed, and if the shaded region is above or below the parabola. y > - x x y - x 2 - x Opens Axis of Symmetry: Opens Axis of Symmetry: Vertex: (, ) Min/Max Value: y-intercept: (, ) Vertex: (, ) Min/Max Value: y-intercept: (, ) A Be able to solve quadratic inequalities using a table and a graph Solve the following inequalities by using a graph and a table. 22. x 2-4x + 1 > x 2 + 2x X Y1 Y2 X Y1 Y2

5 A Be able to solve quadratic inequalities using algebra Solve the following inequalities using algebra. (Hint: Factor) 24. x 2 + 4x x 2-8x < 0 A Be able to determine if a set of data is quadratic Determine if the following data set could represent a quadratic function x y x y

6 A Be able to write a quadratic function from a given set of points Write a quadratic function that fits each set of points using a matrix equation. 28. (0,4), (2,0), and (3,1) 29. (1,3), (2,5), and (4,3) A Be able to use quadratic models to analyze data and predict outcomes 30. Use the table of maximum load allowances for various heights of spruce columns. Find a quadratic regression equation to model the maximum Maximum Load Allowance load given the height. No. 1 Common Spruce Use your model to predict the maximum load allowed for a 6.5 ft spruce column. Use your model to predict the maximum load allowed for an 8 ft spruce column. Height of Column (ft) Maximum Load (lb)