Algebra Pre-Algebra and Basic Algebra Math Forum

 August 19th, 2012, 12:00 AM #1 Senior Member   Joined: Apr 2008 Posts: 194 Thanks: 3 how to do it algebraically? Let's consider the following problem. The range of the function y = square root of f(x) is y = > 4. If f(x) = 0.5*(x + 1)^2 + k. What is k? The vertex of this parabola is (-1,k). Since the minimum value of the range of the square root function is y=4, we can square it to find the y coordinate of the parabola's vertex. So, the answer is k=16. I am sure this answer is correct. My friend asks me whether I can find k=16 algebraically. This is how I start it but can see a complication in my analysis. y = square root of [ 0.5*(x+1)^2 + k ] = > 4 August 19th, 2012, 01:26 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,753 Thanks: 2136 As 0.5*(x+1)� and ?(0.5*(x+1)� + k) are minimized when x = -1, put x = -1 to get ?k = 4, i.e. k = 16. That finds k by an algebraic method. Tags algebraically Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post PhizKid Calculus 6 September 2nd, 2012 08:38 AM drewm Algebra 2 July 4th, 2011 03:06 PM daywalker2day Elementary Math 3 November 15th, 2010 11:13 AM John Creighton Abstract Algebra 0 September 27th, 2010 12:40 PM symmetry Algebra 3 June 12th, 2007 07:56 AM

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