document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=391122>Question 391122</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do i find all the important information(vertex, co vertices ect.) to <BR>\n" );
document.write( "(x-2)2 + (y-2)2 = 1<BR>\n" );
document.write( "_____    _______  <BR>\n" );
document.write( "  16       4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #277441 by </B><A HREF=/tutors/aboutme.mpl?userid=haileytucki><B>haileytucki(390)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=haileytucki><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=haileytucki><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=277441\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "/= + -  and ~= square root\r<BR>\n" );
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document.write( "((x-2)^(2))/(16)+((y-2)^(2))/(4)=1\r<BR>\n" );
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document.write( "Multiply each term by a factor of 1 that will equate all the denominators.  In this case, all terms need a denominator of 16. The ((y-2)^(2))/(4) expression needs to be multiplied by ((4))/((4)) to make the denominator 16.<BR>\n" );
document.write( "((x-2)^(2))/(16)+((y-2)^(2))/(4)*(4)/(4)=1\r<BR>\n" );
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document.write( "Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 16.<BR>\n" );
document.write( "((x-2)^(2))/(16)+((y-2)^(2)(4))/(16)=1\r<BR>\n" );
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document.write( "The numerators of expressions that have equal denominators can be combined.  In this case, ((x-2)^(2))/(16) and (((y-2)^(2)(4)))/(16) have the same denominator of 16, so the numerators can be combined.<BR>\n" );
document.write( "((x-2)^(2)+((y-2)^(2)(4)))/(16)=1\r<BR>\n" );
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document.write( "Simplify the numerator of the expression.<BR>\n" );
document.write( "(x^(2)-4x+4y^(2)-16y+20)/(16)=1\r<BR>\n" );
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document.write( "Multiply each term in the equation by 16.<BR>\n" );
document.write( "(x^(2)-4x+4y^(2)-16y+20)/(16)*16=1*16\r<BR>\n" );
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document.write( "Simplify the left-hand side of the equation by canceling the common factors.<BR>\n" );
document.write( "x^(2)-4x+4y^(2)-16y+20=1*16\r<BR>\n" );
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document.write( "Multiply 1 by 16 to get 16.<BR>\n" );
document.write( "x^(2)-4x+4y^(2)-16y+20=16\r<BR>\n" );
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document.write( "To set the left-hand side of the equation equal to 0, move all the expressions to the left-hand side.<BR>\n" );
document.write( "x^(2)-4x+4y^(2)-16y+4=0\r<BR>\n" );
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document.write( "Use the quadratic formula to find the solutions.  In this case, the values are a=1, b=-4, and c=4y^(2)-16y.<BR>\n" );
document.write( "x=(-b\~(b^(2)-4ac))/(2a) where ax^(2)+bx+c=0\r<BR>\n" );
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document.write( "Use the standard form of the equation to find a, b, and c for this quadratic.<BR>\n" );
document.write( "a=1, b=-4, and c=4y^(2)-16y\r<BR>\n" );
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document.write( "Substitute in the values of a=1, b=-4, and c=4y^(2)-16y.<BR>\n" );
document.write( "x=(-(-4)\~((-4)^(2)-4(1)(4y^(2)-16y)))/(2(1))\r<BR>\n" );
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document.write( "Multiply -1 by each term inside the parentheses.<BR>\n" );
document.write( "x=(4\~((-4)^(2)-4(1)(4y^(2)-16y)))/(2(1))\r<BR>\n" );
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document.write( "Simplify the section inside the radical.<BR>\n" );
document.write( "x=(4\4~(-1(y^(2)-4y-1)))/(2(1))\r<BR>\n" );
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document.write( "Simplify the denominator of the quadratic formula.<BR>\n" );
document.write( "x=(4\4~(-1(y^(2)-4y-1)))/(2)\r<BR>\n" );
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document.write( "First, solve the + portion of \.<BR>\n" );
document.write( "x=(4+4~(-1(y^(2)-4y-1)))/(2)\r<BR>\n" );
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document.write( "Simplify the expression to solve for the + portion of the \.<BR>\n" );
document.write( "x=2+2~(-1(y^(2)-4y-1))\r<BR>\n" );
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document.write( "Next, solve the - portion of \.<BR>\n" );
document.write( "x=(4-4~(-1(y^(2)-4y-1)))/(2)\r<BR>\n" );
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document.write( "Simplify the expression to solve for the - portion of the \.<BR>\n" );
document.write( "x=2-2~(-1(y^(2)-4y-1))\r<BR>\n" );
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document.write( "The final answer is the combination of both solutions.<BR>\n" );
document.write( "x=2+2~(-1(y^(2)-4y-1)),2-2~(-1(y^(2)-4y-1))\r<BR>\n" );
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document.write( "The domain of an expression is all real numbers except for the regions where the expression is undefined.  This can occur where the denominator equals 0, a square root is less than 0, or a logarithm is less than or equal to 0.  All of these are undefined and therefore are not part of the domain.<BR>\n" );
document.write( "(-1(y^(2)-4y-1))<0\r<BR>\n" );
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document.write( "Solve the equation to find where the original expression is undefined.<BR>\n" );
document.write( "y<2-~(5) or y>2+~(5)\r<BR>\n" );
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document.write( "The domain of the rational expression is all real numbers except where the expression is undefined.<BR>\n" );
document.write( "2-~(5) <y<2+~(5)\r<BR>\n" );
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document.write( "The domain of the inverse of ((x-2)^(2))/(16)+((y-2)^(2))/(4)=1 is equal to the range of f(y)=2+2~(-1(y^(2)-4y-1)).<BR>\n" );
document.write( "Range: 2-~(5) <y<2+~(5)\r<BR>\n" );
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document.write( "Now, finding the x and y intercepts:\r<BR>\n" );
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document.write( "((x-2)^(2))/(16)+((y-2)^(2))/(4)=1\r<BR>\n" );
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document.write( "To find the x-intercept, substitute in 0 for y and solve for x.<BR>\n" );
document.write( "((x-2)^(2))/(16)+(((0)-2)^(2))/(4)=1\r<BR>\n" );
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document.write( "Remove the parentheses around the expression 0.\r<BR>\n" );
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document.write( "((x-2)^(2))/(16)+((0-2)^(2))/(4)=1\r<BR>\n" );
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document.write( "Combine all similar expressions.<BR>\n" );
document.write( "((x-2)^(2))/(16)+((-2)^(2))/(4)=1\r<BR>\n" );
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document.write( "Squaring an expression is the same as multiplying the expression by itself 2 times.<BR>\n" );
document.write( "((x-2)^(2))/(16)+((-2)(-2))/(4)=1\r<BR>\n" );
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document.write( "Multiply -2 by -2 to get 4.<BR>\n" );
document.write( "((x-2)^(2))/(16)+(4)/(4)=1\r<BR>\n" );
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document.write( "Reduce the expression (4)/(4) by removing a factor of 4 from the numerator and denominator.<BR>\n" );
document.write( "((x-2)^(2))/(16)+1=1\r<BR>\n" );
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document.write( "Multiply each term by a factor of 1 that will equate all the denominators.  In this case, all terms need a denominator of 16.<BR>\n" );
document.write( "((x-2)^(2))/(16)+1*(16)/(16)=1\r<BR>\n" );
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document.write( "Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 16.<BR>\n" );
document.write( "((x-2)^(2))/(16)+(1*16)/(16)=1\r<BR>\n" );
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document.write( "Multiply 1 by 16 to get 16.<BR>\n" );
document.write( "((x-2)^(2))/(16)+(16)/(16)=1\r<BR>\n" );
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document.write( "The numerators of expressions that have equal denominators can be combined.  In this case, ((x-2)^(2))/(16) and ((16))/(16) have the same denominator of 16, so the numerators can be combined.<BR>\n" );
document.write( "((x-2)^(2)+(16))/(16)=1\r<BR>\n" );
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document.write( "Simplify the numerator of the expression.<BR>\n" );
document.write( "(x^(2)-4x+20)/(16)=1\r<BR>\n" );
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document.write( "Multiply each term in the equation by 16.<BR>\n" );
document.write( "(x^(2)-4x+20)/(16)*16=1*16\r<BR>\n" );
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document.write( "Simplify the left-hand side of the equation by canceling the common factors.<BR>\n" );
document.write( "x^(2)-4x+20=1*16\r<BR>\n" );
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document.write( "Multiply 1 by 16 to get 16.<BR>\n" );
document.write( "x^(2)-4x+20=16\r<BR>\n" );
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document.write( "To set the left-hand side of the equation equal to 0, move all the expressions to the left-hand side.<BR>\n" );
document.write( "x^(2)-4x+4=0\r<BR>\n" );
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document.write( "In this problem -2*-2=4 and -2-2=-4, so insert -2 as the right hand term of one factor and -2 as the right-hand term of the other factor.<BR>\n" );
document.write( "(x-2)(x-2)=0\r<BR>\n" );
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document.write( "Combine the two common factors of (x-2) by adding the exponents.<BR>\n" );
document.write( "(x-2)^(2)=0\r<BR>\n" );
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document.write( "Set each of the factors of the left-hand side of the equation equal to 0.<BR>\n" );
document.write( "x-2=0\r<BR>\n" );
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document.write( "Since -2 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 2 to both sides.<BR>\n" );
document.write( "x=2\r<BR>\n" );
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document.write( "To find the y-intercept, substitute in 0 for x and solve for y.<BR>\n" );
document.write( "(((0)-2)^(2))/(16)+((y-2)^(2))/(4)=1\r<BR>\n" );
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document.write( "Remove the parentheses around the expression 0.<BR>\n" );
document.write( "((0-2)^(2))/(16)+((y-2)^(2))/(4)=1\r<BR>\n" );
document.write( "\n" );
document.write( "Combine all similar expressions.<BR>\n" );
document.write( "((-2)^(2))/(16)+((y-2)^(2))/(4)=1\r<BR>\n" );
document.write( "\n" );
document.write( "Squaring an expression is the same as multiplying the expression by itself 2 times.<BR>\n" );
document.write( "((-2)(-2))/(16)+((y-2)^(2))/(4)=1\r<BR>\n" );
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document.write( "Multiply -2 by -2 to get 4.<BR>\n" );
document.write( "(4)/(16)+((y-2)^(2))/(4)=1\r<BR>\n" );
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document.write( "Reduce the expression (4)/(16) by removing a factor of 4 from the numerator and denominator.<BR>\n" );
document.write( "(1)/(4)+((y-2)^(2))/(4)=1\r<BR>\n" );
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document.write( "The numerators of expressions that have equal denominators can be combined.  In this case, (1)/(4) and ((y-2)^(2))/(4) have the same denominator of 4, so the numerators can be combined.<BR>\n" );
document.write( "(1+(y-2)^(2))/(4)=1\r<BR>\n" );
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document.write( "Simplify the numerator of the expression.<BR>\n" );
document.write( "(y^(2)-4y+5)/(4)=1\r<BR>\n" );
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document.write( "Multiply each term in the equation by 4.<BR>\n" );
document.write( "(y^(2)-4y+5)/(4)*4=1*4\r<BR>\n" );
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document.write( "Simplify the left-hand side of the equation by canceling the common factors.<BR>\n" );
document.write( "y^(2)-4y+5=1*4\r<BR>\n" );
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document.write( "Multiply 1 by 4 to get 4.<BR>\n" );
document.write( "y^(2)-4y+5=4\r<BR>\n" );
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document.write( "To set the left-hand side of the equation equal to 0, move all the expressions to the left-hand side.<BR>\n" );
document.write( "y^(2)-4y+1=0\r<BR>\n" );
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document.write( "Use the quadratic formula to find the solutions.  In this case, the values are a=1, b=-4, and c=1.<BR>\n" );
document.write( "y=(-b\~(b^(2)-4ac))/(2a) where ay^(2)+by+c=0\r<BR>\n" );
document.write( "\n" );
document.write( "Use the standard form of the equation to find a, b, and c for this quadratic.<BR>\n" );
document.write( "a=1, b=-4, and c=1\r<BR>\n" );
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document.write( "Substitute in the values of a=1, b=-4, and c=1.<BR>\n" );
document.write( "y=(-(-4)\~((-4)^(2)-4(1)(1)))/(2(1))\r<BR>\n" );
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document.write( "Multiply -1 by each term inside the parentheses.<BR>\n" );
document.write( "y=(4\~((-4)^(2)-4(1)(1)))/(2(1))\r<BR>\n" );
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document.write( "Simplify the section inside the radical.<BR>\n" );
document.write( "y=(4\2~(3))/(2(1))\r<BR>\n" );
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document.write( "Simplify the denominator of the quadratic formula.<BR>\n" );
document.write( "y=(4\2~(3))/(2)\r<BR>\n" );
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document.write( "First, solve the + portion of \.<BR>\n" );
document.write( "y=(4+2~(3))/(2)\r<BR>\n" );
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document.write( "Simplify the expression to solve for the + portion of the \.<BR>\n" );
document.write( "y=2+~(3)\r<BR>\n" );
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document.write( "Next, solve the - portion of \.<BR>\n" );
document.write( "y=(4-2~(3))/(2)\r<BR>\n" );
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document.write( "Simplify the expression to solve for the - portion of the \.<BR>\n" );
document.write( "y=2-~(3)\r<BR>\n" );
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document.write( "Solve the equation.<BR>\n" );
document.write( "y=2+~(3),2-~(3)\r<BR>\n" );
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document.write( "These are the x and y intercepts of the equation ((x-2)^(2))/(16)+((y-2)^(2))/(4)=1.<BR>\n" );
document.write( "x=2, y=2+~(3),2-~(3)\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );