document.write( "Question 889068: Find \"a\" such that \"f%28x%29=ax%5E2%2B5x%2B6\" has a minimum value of \"169%2F24\" \n" ); document.write( "
Algebra.Com's Answer #537875 by MathTherapy(10559)\"\" \"About 
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Find \"a\" such that \"f%28x%29=ax%5E2%2B5x%2B6\" has a minimum value of \"169%2F24\"
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document.write( "(h, k) is the coordinate point of the vertex of the parabola
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document.write( "h , or x-coordinate of vertex = \"-+b%2F2a\", or \"-+5%2F2a\"\r
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document.write( "\"y+=+ax%5E2+%2B+5x+%2B+6\", with \"x+=+-+5%2F2a\"
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document.write( "k, or y-coordinate of vertex = \"a%28-+5%2F2a%29%5E2+%2B+5%28-+5%2F2a%29+%2B+6\"
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document.write( "\"k+=+a%2825%2F4a%5E2%29+%2B+-+25%2F2a+%2B+6\"
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document.write( "\"k+=+25a%2F4a%5E2+-+25%2F2a+%2B+6\"    
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document.write( "\"k+=+25%2F4a+-+25%2F2a+%2B+6\"
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document.write( "\"k+=+%2825+-+50+%2B+24a%29%2F4a\" ------ Multiplying right-side by LCD, 4a
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document.write( "\"k+=+%28-+25+%2B+24a%29%2F4a\"   \r
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document.write( "Since \"k+=+%28-+25+%2B+24a%29%2F4a\", and minimum value = \"169%2F24\", then: \"%28-+25+%2B+24a%29%2F4a+=+169%2F24\"
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document.write( "169(4a)  = 24(- 25 + 24a) ------ Cross-multiplying
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document.write( "676a = - 600 + 576a
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document.write( "676a – 576a = - 600
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document.write( "100a = - 600
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document.write( "\"a+=+%28-+600%29%2F100\", or \"highlight_green%28highlight_green%28a+=+-+6%29%29\"
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document.write( "Since a = - 6, then this equation DOES NOT DEPICT a minimum, but a maximum instead, as a < 0.\r
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document.write( "You can do the check!! \r
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document.write( "Send comments, “thank-yous,” and inquiries to “D” at MathMadEzy@aol.com.
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document.write( "Further help is available, online or in-person, for a fee, obviously. \r
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