nomial and Rational Functions 22. Concept Check A quadratic function f(x) has vertex (0, 0), and all of its intercepts are the same point. What is the general form of its equation? Graph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. Then determine (e) the largest open interval of the domain over which the function is increasing and (f) the largest open interval over which the function is decreasing. See Examples 1-4 23. f(x) = (x - 2)2 24. f(x) (x + 4)2 25. f(x) = (x + 3)2 - 4 26. f(x) (x - 5)2 - 4 11 27. f(x) (x + 1)2 - 3 28. f(x)3(x - 2)2 +1 29. f(x) = x2- 2x + 3 30. f(x) = x2 +6x + 5 31. f(x)= x2 - 10x + 21 32. f(x) 2x2- 4x + 5 1 33. f(x)=-2x2- 12x- 16 34. f(x)=-3x224x 46 5 35. f(x)= 2- 2 x2-3x- 36. f(x) x2 3 3 3 Concept Check The figure shows the graph of a quadratic function y f (x). Use it to answer each question. y 1 'y = f( 37. What is the minimum value of f(x)? 38. For what value of x is f(x) as small as possible? 3 (-3, 3) 39. How many real solutions are there to the equation f(x) = 1? + -3 40. How many real solutions are there to the equation f(x) = 4? Concept Check Several graphs of the quadratic function f(x) = ax2 + bx + c ++ - |C

nomial and Rational Functions 22. Concept Check A quadratic function f(x) has vertex (0, 0), and all of its intercepts are the same point. What is the general form of its equation? Graph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. Then determine (e) the largest open interval of the domain over which the function is increasing and (f) the largest open interval over which the function is decreasing. See Examples 1-4 23. f(x) = (x - 2)2 24. f(x) (x + 4)2 25. f(x) = (x + 3)2 - 4 26. f(x) (x - 5)2 - 4 11 27. f(x) (x + 1)2 - 3 28. f(x)3(x - 2)2 +1 29. f(x) = x2- 2x + 3 30. f(x) = x2 +6x + 5 31. f(x)= x2 - 10x + 21 32. f(x) 2x2- 4x + 5 1 33. f(x)=-2x2- 12x- 16 34. f(x)=-3x224x 46 5 35. f(x)= 2- 2 x2-3x- 36. f(x) x2 3 3 3 Concept Check The figure shows the graph of a quadratic function y f (x). Use it to answer each question. y 1 'y = f( 37. What is the minimum value of f(x)? 38. For what value of x is f(x) as small as possible? 3 (-3, 3) 39. How many real solutions are there to the equation f(x) = 1? + -3 40. How many real solutions are there to the equation f(x) = 4? Concept Check Several graphs of the quadratic function f(x) = ax2 + bx + c ++ - |C

Name: How do you answer 32? nomial and Rational Functions22. Concept Check A
Uploaded: 2024-03-20T07:06:16.000Z
Channel: Bartleby
Description: How do you answer 32? nomial and Rational Functions22. Concept Check A quadratic function f(x) has vertex (0, 0), and all of its interceptsare the same point. What is the general form of its equation?Graph each quadratic function. Give the (a) vertex

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter3: Polynomial And Rational Functions

Section: Chapter Questions

Problem 1CC: (a) What is the degree of a quadratic function f?What is the standard form of a quadratic function?...

See similar textbooks

Similar questions

Height of a football A football is thrown by a quarterback from the 10-yard line and caught by the wide receiver on the 50-yard line. The footballs path on this interval can be modeled by the quadratic function f(x)=120x2+3x19, where x is the horizontal distance in yards from the goal line and f(x) is the height of the football in feet. Find the maximum height reached by the football.
Writing an Equation The graph of a fourth-degree polynomial function y=fx is shown. The equation has 2i as zeros. Write an equation for f.
Local extrema these exercises involve local maximaand minima of polynomial functions. Graph the function P(x)=(x2)(x4)(x5) and determine how many local extrema it has. If a < b < c, explain why the function P(x)=(xa)(xb)(xc) must have two local extrema-
Revenue A manufacturer finds that the revenue generated by selling x units of a certain commodity is given by the function R(x)=80x0.4x2, where the revenue R(x) is measured in dollars. What is the maximum revenue? and how many units should be manufactured to obtain this maximum?
Graphs of Quadratic Functions A quadratic function isgiven. (a) Express the function in standard form. (b) Graph the Function. f(x)=2x28x+4
Volume of a Box An open box is to constructed from a piece of cardboard 20 cm by 40 cm by cutting squares of side length x from each corner and folding up the sides, as shownin figure. (a) Express the volume V of the box as a function of x. (b) What is the domain of V? (Use the fact that length and volume must be positive.) (c) Draw a graph of the function V, and use it to estimate the maximum volume for such a box.
Graphs of Quadratic Functions The graph of a quadratic function f is given. (a) Find the coordinates of the vertex and the x and y-intercept. (b) Find the maximum or minimum value of f . (c) Find the domain and range of f . f(x)=2x24x1