AlgebraDate: 5/10/96 at 10:26:55 From: Anonymous Subject: Algebra Find the domain, range, and zeros of g(x) = x^2 - 6x + 4 Date: 10/17/96 at 12:51:17 From: Doctor Leigh Subject: Re: Algebra The domain of a function is all the values of x that can be put into the function. In this case the domain is all real numbers. The range of the function is all the values of Y that the function covers. This function has a range of y >= -5. The zeros of a function are found by setting the function equal to zero and solving for x. The zeros of this function are 3 + sqrt(5) and 3 - sqrt(5) Use the quadratic equation. -Doctor Leigh Ann, The Math Forum Check out our web site! http://mathforum.org/dr.math/ Date: 09/01/2000 at 17:58:48 From: Tim Greene Subject: Algebra Hello Dr. Math: I would like to expand upon the solution given for a problem in your archives. In this problem, the writer states that the range of the function x^2 - 6x + 4 is y >= -5. No method is shown for obtaining this result. I assume the writer determined the function had a minimum value when x = 3 and substituted that value of x in the function to find the lower limit of the range for the function. Of course calculus shows us quickly that the minimum value is when x = 3; however, many high school students will not know calculus. The value of x for which the function has a minimum, and that minimum value, can both be obtained by completing the square in the given function; most second year algebra students and many first year algebra students will be able to understand this approach. y = x^2 is a parabola opening upwards with vertex at (0,0); y = x^2 + k is a parabola opening upwards with vertex at (0,k); and y = (x-h)^2 + k is a parabola opening upwards with vertex at (h,k) Therefore, g(x) = x^2 - 6x + 4 = (x^2 - 6x + 9) - 5 = (x-3)^2 - 5 is a parabola with vertex (3,-5), so the range of the function is [-5,infintiy] or y >= -5. Tim Greene |
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