document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=166890>Question 166890</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if y=2x(squared)+6x+1 what are the coeffecients, what is the vertex of the parabola, what is the axis of symmetry, what is the y-intercept, and if it is reflected across the y-intercept across the axis of symmetry x=_____, x=______\r<BR>\n" );
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document.write( "pleas help i'm in jeapordy of failing. contact me- for subject put alg 2\r<BR>\n" );
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document.write( "o and we do nnot use a textbook to do work. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #122964 by </B><A HREF=/tutors/aboutme.mpl?userid=MRperkins><B>MRperkins(300)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MRperkins><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=MRperkins><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=122964\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here are some book definitions for you:<BR>\n" );
document.write( "A MONOMIAL is a real number, a variable, or a product of real numbers adn variables.  The expressions -15, 3z and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7x%5E3y%5E5z ALIGN=MIDDLE  ALT=\"-7x%5E3y%5E5z\"   DISABLED_style= \"max-width:90%; height:auto;\" > are all monomials.<BR>\n" );
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document.write( "The COEFFICIENT of a monomial is its numerical factor.  For example, the coefficient in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2.8x%5E7y%5E3z ALIGN=MIDDLE  ALT=\"-2.8x%5E7y%5E3z\"   DISABLED_style= \"max-width:90%; height:auto;\" > is -2.8.<BR>\n" );
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document.write( "The DEGREE OF A MONOMIAL is the sum of the exponents of the monomial's variables.  The degree of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2.8x%5E7y%5E3z ALIGN=MIDDLE  ALT=\"-2.8x%5E7y%5E3z\"   DISABLED_style= \"max-width:90%; height:auto;\" > is 11 because 7+3+1=11.<BR>\n" );
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document.write( "A POLYNOMIAL is an expression that is either a monomial or a sum or difference of monomials.  Each monomial component of a polynomial is called a TERM.  The terms of a polynomail are usually arranged in descending order of powers.  <BR>\n" );
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document.write( "The LEADING COEFFICIENT of a polynomial is the coefficient of the first term when the polynomial is written in descentding order of powers.  For example, the leading coefficient of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E3%2B5x%2B2 ALIGN=MIDDLE  ALT=\"-x%5E3%2B5x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is -1.<BR>\n" );
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document.write( "The DEGREE OF A POLYNOMIAL is equal to the greatest of the degrees of the polynomial's terms.  Polynomials are classified by their degree and by thier number of terms.  The polynomial <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E3%2B5x%2B2 ALIGN=MIDDLE  ALT=\"-x%5E3%2B5x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is classified as a cubic(degree-three) trinomial.  The polynomial <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-17 ALIGN=MIDDLE  ALT=\"y%5E2-17\"   DISABLED_style= \"max-width:90%; height:auto;\" > is an example of a quadratic (degree-two) binomial.<BR>\n" );
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document.write( "I know this may sound like a lot but it is only 6 or 7 definitions and if you understand these definitions then all of this will be much easier to understand.  <BR>\n" );
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document.write( "the coefficients are simply the number(1,2,3...) in front of a variable(a,b,x,y,...)<BR>\n" );
document.write( "so the coefficients in this problem are 2,6, and 1. <BR>\n" );
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document.write( "In order to find the vertex of the parabola we need to put the equation in vertex form.<BR>\n" );
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document.write( "VERTEX FORM:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"f%28x%29=a%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "By using a process called COMPLETING THE SQUARE, we can rewrite a quadratic function of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"f%28x%29=ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"f%28x%29=a%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Write your problem <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2x%5E2%2B6x%2B1 ALIGN=MIDDLE  ALT=\"f%28x%29=2x%5E2%2B6x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > in VERTEX FORM.<BR>\n" );
document.write( "We want to rewrite the quadratic expression so that it contains a trinomial of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2ax%2Ba%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2B2ax%2Ba%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >--the square of a binomial x+a.  To do so, WE ADD TO THE FIRST TWO TERMS THE SQUARE OF HALF THE LINEAR COEFFICIENT. THEN, SO THAT WE DO NOT CHANGE THE VALUE OF THE EXPRESSION, WE MUST SUBTRACT THE SAME VALUE.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2x%5E2%2B6x%2B1 ALIGN=MIDDLE  ALT=\"f%28x%29=2x%5E2%2B6x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factor out the 2. (the leading coefficient must always be 1 for the complete the square method to work)  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2%28x%5E2%2B3x%29%2B1 ALIGN=MIDDLE  ALT=\"f%28x%29=2%28x%5E2%2B3x%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "rewrite, leaving space to add and subtract a quantitiy. f(x)=2(x^2+3x+___)-____+1<BR>\n" );
document.write( "Complete the square by adding and subtracting (1/2 *3)^2.  Because we had to factor out the two, we need to multiply (9/4) by 2 in order to keep the equation equal (this part is tough to explain in writing so if you do not understand it then email me and I will call you):  f(x)=2(x^2+3x+(9/4))-2(9/4)+1<BR>\n" );
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document.write( "Factor the perfect-square trinomial and add the constants <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2%28x%2B%283%2F2%29%29%5E2-4.5%2B1 ALIGN=MIDDLE  ALT=\"f%28x%29=2%28x%2B%283%2F2%29%29%5E2-4.5%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2%28x%2B%283%2F2%29%29%5E2-3.5 ALIGN=MIDDLE  ALT=\"f%28x%29=2%28x%2B%283%2F2%29%29%5E2-3.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The vertex is going to be the value of x when (x+(3/2))=0<BR>\n" );
document.write( "so the vertex is x=(-3/2).<BR>\n" );
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document.write( "It is reflected across the line x=-3/2 and intersects the x-axis at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%2B-sqrt%287%29%29%2F2 ALIGN=MIDDLE  ALT=\"%28-3%2B-sqrt%287%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C2x%5E2%2B6x%2B1%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C2x%5E2%2B6x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "I hope this helps!<BR>\n" );
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document.write( "Private tutoring is available.  Click on my name to go to my website or email me at justin.sheppard.tech@hotmail.com for more information.  If you have any other questions you can direct them to me personally and I will answer them for you.\r<BR>\n" );
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