document.write( "Question 51314: f(x)=x^2+6x+5\r
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Algebra.Com's Answer #34251 by AnlytcPhil(1810)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "am I correct?\r\n" );
document.write( "f(x) = x² + 6x + 5\r\n" );
document.write( "What is the y- intercept of this function? \r\n" );
document.write( "My ans is (5,0) \r\n" );
document.write( "am I correct?\r\n" );
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document.write( "No.  You have it backwards.  It's (0,5).  Remember, it's x that \r\n" );
document.write( "you replace by 0 to find the y-intercept.  You do know, don't you, \r\n" );
document.write( "that f(x) is exactly the same thing as y? \r\n" );
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document.write( "In other words there is no difference between\r\n" );
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document.write( "f(x) = x² + 6x + 5 \r\n" );
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document.write( "and\r\n" );
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document.write( "   y = x² + 6x + 5\r\n" );
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document.write( "f(x) is only a different way of writing y. So when you\r\n" );
document.write( "plug in 0 for x, you get\r\n" );
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document.write( "   y = 0² + 6(0) + 5\r\n" );
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document.write( "   y = 5\r\n" );
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document.write( "So it's (0,5) [and NOT (5,0)! That's important!] \r\n" );
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document.write( "Remember, that x comes before y in the alphabet, and you\r\n" );
document.write( "can use that fact to remember that what you substitute\r\n" );
document.write( "for x comes first and what you get for y, comes second\r\n" );
document.write( "in the ordered pair that represents the point.  It is\r\n" );
document.write( "important not to get these backward.\r\n" );
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document.write( "and what is the zero's of this parabola? \r\n" );
document.write( "My ans is (0,-1),(0,-5) \r\n" );
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document.write( "That's wrong, You have those backwards too.\r\n" );
document.write( "Remember that x comes before y in the alphabet.\r\n" );
document.write( "It's (x,y), and not (y,x)! So the x-intercepts\r\n" );
document.write( "are the points (-1,0) and (-5,0).  But that's\r\n" );
document.write( "not all you are getting wrong. You are calling \r\n" );
document.write( "points represented by ordered pair \"zeros\". \r\n" );
document.write( "This is wrong, too. \r\n" );
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document.write( "Now let's go through this and see if I can\r\n" );
document.write( "straighten you out.  Your difficulty is not\r\n" );
document.write( "with the algebra manipulation. You do that \r\n" );
document.write( "correctly. Your difficulty is with the words\r\n" );
document.write( "and what they mean, and with the notation.\r\n" );
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document.write( "The x-intercepts are found by substituting 0 \r\n" );
document.write( "for f(x) or y, and solving.\r\n" );
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document.write( "You apparently did this correctly:\r\n" );
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document.write( "                   y = x² + 6x + 5\r\n" );
document.write( "                   0 = x² + 6x + 5\r\n" );
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document.write( "It looks better when you put the = 0 on the right\r\n" );
document.write( "instead of the left:\r\n" );
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document.write( "             x² + 6x + 5 = 0\r\n" );
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document.write( "          (x + 1)(x + 5) = 0\r\n" );
document.write( "  \r\n" );
document.write( "Setting x + 1 = 0 gives x = -1\r\n" );
document.write( "Setting x + 5 = 0 gives x = -5\r\n" );
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document.write( "But you got the coordinates backward.  Notice that \r\n" );
document.write( "the value you substituted for y, namely 0,\r\n" );
document.write( "is supposed to be written SECOND and the x-value is \r\n" );
document.write( "written FIRST.  So the x-intercepts are (-1,0) and \r\n" );
document.write( "(-5,0). Don't get the x-value and the y-value \r\n" );
document.write( "backward.  When you substitute 0 for x, you write 0 \r\n" );
document.write( "first like this (0,___) and you then fill in the blank \r\n" );
document.write( "with what you end up getting for y. And when you \r\n" );
document.write( "substitute 0 for y, you write 0 second like this \r\n" );
document.write( "(___, 0) and you fill in the blank with what you end \r\n" );
document.write( "up getting for x. \r\n" );
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document.write( "Now also I need to tell you the difference between \"zeros\" \r\n" );
document.write( "and \"x-intercepts\".  They are certainly related! But a zero\r\n" );
document.write( "of a function is just a SINGLE NUMBER.  It's not a point \r\n" );
document.write( "and it's not an ordered pair like (-1,0) and (-5,0). What \r\n" );
document.write( "we call the \"zeros\" are just the x-coordinates of these \r\n" );
document.write( "x-intercept points, not the whole points.  The \"zeros\" are \r\n" );
document.write( "just the numbers -1 and -5, not the x-intercept points\r\n" );
document.write( "(-1,0) and (-5,0).  You see the difference, right?  Yes,\r\n" );
document.write( "math is picky!  :-)  \r\n" );
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document.write( "I hope this helps you get these things straight.\r\n" );
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document.write( "Edwin
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