document.write( "Question 1202232: If the parabola has equation y = 2(x - 4)? - 1 as a base function, write an equation for the
\n" ); document.write( "parabola if there is a reflection in the x-axis followed by a translation of 3 units upwards. \n" ); document.write( "

Algebra.Com's Answer #836906 by ikleyn(52798) $\"\"$ $\"About$

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\n" ); document.write( "If the parabola has equation y = 2(x-4)^2 - 1 as a base function, write an equation for the
\n" ); document.write( "parabola if there is a reflection in the x-axis followed by a translation of 3 units upwards.
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document.write( "First, reflection in the x-axis turns the function into\r\n" );
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document.write( "    y = -2(x-4)^2 + 1.\r\n" );
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document.write( "    +---------------------------------------------------------------+\r\n" );
document.write( "    |   It simply changes the sign of all terms in the right side.  |\r\n" );
document.write( "    +---------------------------------------------------------------+\r\n" );
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document.write( "So, after this transformation our function is\r\n" );
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document.write( "    y = -2(x-4)^2 + 1.    (1)\r\n" );
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document.write( "The translation of 3 units upwards adds 3 to the function (1),\r\n" );
document.write( "so after this translation your function is\r\n" );
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document.write( "    y = -2(x-4)^2 + 4.    ANSWER\r\n" );
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