University:
Glendale Community College
Course:
MAT150 | College Algebra/Functions
Academic year:

2020
Views:

456

Pages:

16
Author:

Deandre Simmons

Section 4.3: Quadratic functions and their properties #1-12: For each problem do the following 1) f(x - 3) + 4 a) Find the indicated function and describe the transformation as compared to the function f(x) = x2, specifically state if the graph is shifted left, right, up, down and if any reflection has occurred b) make a table of values and sketch a graph. c) state the domain and range of the function d) state the intervals where the function in increasing and decreasing e) state if the function has a local maximum point, if it does state the local maximum value f) state if the function has a local minimum point, if it does state the local minimum value x f(x) 3) 2f(x+3) - 4 a) Find the indicated function and describe the transformation as compared to the function f(x) = x2, specifically state if the graph is shifted left, right, up, down and if any reflection has occurred b) make a table of values and sketch a graph. c) state the domain and range of the function d) state the intervals where the function in increasing and decreasing e) state if the function has a local maximum point, if it does state the local maximum value f) state if the function has a local minimum point, if it does state the local minimum value x f(x) 5) 1 2 𝑓(𝑥 + 4) − 6 a) Find the indicated function and describe the transformation as compared to the function f(x) = x2, specifically state if the graph is shifted left, right, up, down and if any reflection has occurred b) make a table of values and sketch a graph. c) state the domain and range of the function d) state the intervals where the function in increasing and decreasing e) state if the function has a local maximum point, if it does state the local maximum value f) state if the function has a local minimum point, if it does state the local minimum value x f(x) 7) -2f(x) + 3 a) Find the indicated function and describe the transformation as compared to the function f(x) = x2, specifically state if the graph is shifted left, right, up, down and if any reflection has occurred b) make a table of values and sketch a graph. c) state the domain and range of the function d) state the intervals where the function in increasing and decreasing e) state if the function has a local maximum point, if it does state the local maximum value f) state if the function has a local minimum point, if it does state the local minimum value x f(x) 1 9) − 𝑓(𝑥 + 5) − 2 4 a) Find the indicated function and describe the transformation as compared to the function f(x) = x2, specifically state if the graph is shifted left, right, up, down and if any reflection has occurred b) make a table of values and sketch a graph. c) state the domain and range of the function d) state the intervals where the function in increasing and decreasing e) state if the function has a local maximum point, if it does state the local maximum value f) state if the function has a local minimum point, if it does state the local minimum value x f(x) 11) 2f(x+3)+4 a) Find the indicated function and describe the transformation as compared to the function f(x) = x2, specifically state if the graph is shifted left, right, up, down and if any reflection has occurred b) make a table of values and sketch a graph. c) state the domain and range of the function d) state the intervals where the function in increasing and decreasing e) state if the function has a local maximum point, if it does state the local maximum value f) state if the function has a local minimum point, if it does state the local minimum value x f(x) #13 – 24: For each problem do the following: 13) f(x) = x2 + 6x + 5 a) Use completing the square to rewrite the problem in standard form b) Describe the transformation as compared to the function f(x) = x2 c) Sketch a graph, make sure to label the vertex. You may use your calculator, instead of making a table of values to create your graph 15) k(x) = x2 – 4x + 2 a) Use completing the square to rewrite the problem in standard form b) Describe the transformation as compared to the function f(x) = x2 c) Sketch a graph, make sure to label the vertex. You may use your calculator, instead of making a table of values to create your graph 17) f(x) = 2x2 + 8x – 3 a) Use completing the square to rewrite the problem in standard form b) Describe the transformation as compared to the function f(x) = x2 c) Sketch a graph, make sure to label the vertex. You may use your calculator, instead of making a table of values to create your graph 19) f(x) = -x2 + 6x + 4 a) Use completing the square to rewrite the problem in standard form b) Describe the transformation as compared to the function f(x) = x2 c) Sketch a graph, make sure to label the vertex. You may use your calculator, instead of making a table of values to create your graph 21) k(x) = -2x2 + 12x – 7 a) Use completing the square to rewrite the problem in standard form b) Describe the transformation as compared to the function f(x) = x2 c) Sketch a graph, make sure to label the vertex. You may use your calculator, instead of making a table of values to create your graph 23) f(x) = -3x2 – 12x + 1 a) Use completing the square to rewrite the problem in standard form b) Describe the transformation as compared to the function f(x) = x2 c) Sketch a graph, make sure to label the vertex. You may use your calculator, instead of making a table of values to create your graph #25 – 32, determine the equation of the quadratic function 25) 27) 29) 31)