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# domain and range of a quadratic equation

Question:Question 4 (Essay Worth 6 points) Your friend, Patricia, is having a hard time understanding the concept behind the domain and range of a parabola. Using complete sentences, explain the meaning of the domain and range of the graph of y = x2 + 4x 21 and how to find both. Keep in mind, your goal is to help Patricia understand the "concepts", not just how to use the steps. * PLEASE HELP me with this I have a test tomorrow! THANKS A TON!

Answers:Domain is basically all the numbers that make sense for x. In other words, it is the set of real numbers that will make the function "work" and will give real y-values. The domain for a parabola, like x^2, for example, is all real numbers. This is so because there are all real values of y for every real value of x. Basically, the parabola will hit all values of x at some value of y. In your equation, y = x^2 + 4x - 21, the domain is all real numbers because it is a parabola. Range is the same thing, but for y. So for x^2 again, the range is all real numbers for x>0. You have to have the restriction x>0 because the parabola does not go below zero. You can't have a y-value that is negative in your range, because the parabola is not negative. Think of both the domain and range as numbers that the function allows you to work with. To find the range for your equation, you need to find the minimum value (vertex) of the parabola. The equation is: x = -b/(2a) x = -(4) / (2*(1)) x = -2 Plug the x-value into your equation. y = (-2)^2 + 4(-2) - 21 y = -25 So the range is: -25 ltoet x < infinity (ltoet = less than or equal to, I can't use the symbol on here)

Question:Question 1. What is the domain and range of the quadratic equation y = x2 14x 52? a. Domain: All Real Numbers Range: y 7 b. Domain: All Real Numbers Range: y 7 c. Domain: All Real Numbers Range: y 3 d. Domain: All Real Numbers Range: y 3 Question 2. What are the x and y intercepts of the quadratic equation y = (x 3)2 25? Identify the x intercepts by graphing the quadratic equation. a. x intercepts: ( 2, 0) and (8, 0) y intercept: (0, 16) b. x intercepts: (2, 0) and ( 8, 0) y intercept: (0, 16) c. x intercepts: ( 2, 0) and (8, 0) y intercept: (0, 25) d. x intercepts: (2, 0) and ( 8, 0) y intercept: (0, 25) Question 3. Which of the following is the vertex of the quadratic equation y = 6x2 24x + 32? a. ( 2, 8) b. ( 2, 8) c. (2, 8) d. (2, 8) Question 4. What are the x and y intercepts of the quadratic equation y = 2x2 8x + 6? a. x intercepts: ( 3, 0) and ( 1, 0) y intercept: (0, 3) b. x intercepts: ( 3, 0) and ( 1, 0) y intercept: (0, 6) c. x intercepts: ( 3, 0) and ( 1, 0) y intercept: (0, 3) d. x intercepts: (3, 0) and (1, 0) y intercept: (0, 6) Question 5. Which of the following is the equation of the axis of symmetry of the quadratic equation y = 2x2 + 24x + 62? a. x = 6 b. x = 6 c. x = 10 d. x = 10 Question 6. What is the domain and range of the quadratic equation y = (x 5)2 + 10? a. Domain: All Real Numbers Range: y 5 b. Domain: All Real Numbers Range: y 5 c. Domain: All Real Numbers Range: y 10 d. Domain: All Real Numbers Range: y 10 Question 7. Which of the following is the equation of the axis of symmetry of the quadratic equation y = 2(x + 7)2 4? a. x = 7 b. x = 4 c. x = 4 d. x = 7 Question 8 Which of the following is the vertex of the quadratic equation y = 4(x + 6)2 + 2? a. (6, 2) b. ( 6, 2) c. (6, 2) d. ( 6, 2)

Answers:1) Domain is all real numbers y = x^2 14x 52 y = -(x^2 + 14x + 52) y = -(x^2 + 14x + 49) - 3 y = -(x + 7)^2 - 3 Range is all x <= -3. In set notation, the range is (-infinity, -3].

Question:f(x) = -3x2 + 12x - 8 it says that the answer is this: Domain: (- infinity, infinity) Range: (-infinity, 4] how do you get the domain/range? I know how to get the vertex, which is(-b/2a, f(-b/2a) ) but how do you find the d/r? thanks!!

Answers:The domain is all x. There is no reason any particular x value is not possible. This is a quadratic opening downward, with a maximum y value at the vertex. So y values are not possible greater than that maximum y value.

Question:

Answers:This is a great site: http://www.purplemath.com/modules/ Domain is the "input" ....."x" Range is the "output" ..... "y"

Int Algebra: Finding Domain and Range :www.mindbites.com This lesson is part of a series: Intermediate Algebra While a function always satisfies the vertical line test (for any value of x there is only one value of y), there are functions in which the domain of the function does not include all values of x. In this lesson, we look at the domain of a function (all of the values of x for which we can evaluate the function and find a value of y) and the range of a function (all the values of y that may be generated by evaluating the function for some value of x). In addition to learning about evaluating a function to find the domain and range, Professor Burger will graphically show you how to identify the domain and range.Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Intermediate Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at www.thinkwell.com The full course covers real numbers, equations and inequalities, exponents and polynomials, rational expressions, roots and radicals, relations and functions, the straight line, systems of equations, quadratic equations and quadratic inequalities, conic sections, inverse and exponential and logarithmic functions, and a variety of other AP algebra and advanced algebra.

College Algebra: Domain and Range: An Example :www.mindbites.com Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, College Algebra. This course and others are available from Thinkwell, Inc. The full course can be found atwww.thinkwell.com The full course covers equations and inequalities, relations and functions, polynomial and rational functions, exponential and logarithmic functions, systems of equations, conic sections and a variety of other AP algebra, advanced algebra and Algebra II topics. Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College. He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America". Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences ...