document.write( "Question 1205883: The table shows several input and output values of a quadratic
\n" ); document.write( "function d(t).
\n" ); document.write( "t d(t)
\n" ); document.write( "3 3.00
\n" ); document.write( "4 5.00
\n" ); document.write( "4.5 5.25
\n" ); document.write( "5. 5.00
\n" ); document.write( "6 3.00\r
\n" ); document.write( "\n" ); document.write( "Which statement is true about the function?
\n" ); document.write( "Ⓐ The maximum value of d(t) is 6.
\n" ); document.write( "Ⓑ The axis of symmetry is t = 5.25.
\n" ); document.write( "Ⓒ The range of the function d(t) is 3 < t < 6.
\n" ); document.write( "Ⓓ The function d(t) is increasing when t < 4.5. \n" ); document.write( "

Algebra.Com's Answer #842959 by mccravyedwin(407) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Since d(t) is a quadratic function, it is of the form \r\n" );
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document.write( ". Since we are told that we have 5 solution:\r\n" );
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document.write( "are solutions, we assume they are truthful, pick three\r\n" );
document.write( "of them, and have the system:\r\n" );
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document.write( "Solving that system gives A=-1, B=9, C=-15, and we take their word\r\n" );
document.write( "for it that the other two are solutions, and therefore, the quadratic \r\n" );
document.write( "equation is:\r\n" );
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document.write( "We know it is concave downward, because the leading coefficient A=-1 is\r\n" );
document.write( "negative. So we know it has a maximum value\r\n" );
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document.write( "We use the vertex formula:\r\n" );
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document.write( "(4.5,5.25), so the maximum value is 5.25\r\n" );
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document.write( "So (A) is false.\r\n" );
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document.write( "The axis of symmetry is . \r\n" );
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document.write( "So (B) is false.\r\n" );
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document.write( "The range of the function is from negaive infinity to the maximum value, or\r\n" );
document.write( "the range is \r\n" );
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document.write( "So (C) is false.\r\n" );
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document.write( "The function is neither increasing nor decreasing at its maximum\r\n" );
document.write( "point (4.5,5.25).\r\n" );
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document.write( "So (D) is false.\r\n" );
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document.write( "So they're all false.\r\n" );
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document.write( "Edwin

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