document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1044241>Question 1044241</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am not understanding these at all.  Can someone help me with this example?\r<BR>\n" );
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document.write( "Given the quadratic function f(x) = 3x2 + 6x - 4 <BR>\n" );
document.write( "a. Find the vertex <BR>\n" );
document.write( "b. Find the axis of symmetry <BR>\n" );
document.write( "c. Find the x- and y-intercepts <BR>\n" );
document.write( "d. State the domain and range of the function <BR>\n" );
document.write( "e. Find the interval(s) over which the function is increasing <BR>\n" );
document.write( "f. Find the interval(s) over which the function is decreasing <BR>\n" );
document.write( "g. Graph the function <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #659517 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=659517\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = 3x^2 +6x - 4<BR>\n" );
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document.write( "This is a parabola that curves upward, here is its graph<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-2.8%2C+0.8%2C+-8%2C+4%2C+3x%5E2+%2B6x+-4%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-2.8%2C+0.8%2C+-8%2C+4%2C+3x%5E2+%2B6x+-4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The general form of a polynomial for the given function is<BR>\n" );
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document.write( "f(x) = ax^2 +bx +c, where a, b, c are real numbers<BR>\n" );
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document.write( "The x coordinate for the vertex is given by <BR>\n" );
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document.write( "x = -b /2a, for our given function we have<BR>\n" );
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document.write( "x = -6 / (2 * 3) = -1<BR>\n" );
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document.write( "substitute for x in the given function for the y coordinate of the vertex<BR>\n" );
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document.write( "y = f(x) = 3(-1)^2 +6(-1) -4 = -7<BR>\n" );
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document.write( "a) vertex is at (-1, -7)<BR>\n" );
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document.write( "b) axis of symmetry is x = -1<BR>\n" );
document.write( "half of the parabola is to the left and half of the parabola is to the right <BR>\n" );
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document.write( "The y intercept is found by setting x = 0 and solve for y<BR>\n" );
document.write( "y = 3(0)^2 +6(0) -4 = -4<BR>\n" );
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document.write( "x intercept/s are found by solving the given function for x, when f(x) = 0<BR>\n" );
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document.write( "3x^2 +6x -4 = 0<BR>\n" );
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document.write( "use quadratic formula to solve for x<BR>\n" );
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document.write( "x = (-6 + square root((-6)^2 -4*3*(-4))) / (2(3)) = (-3 + square root(21)) / 3<BR>\n" );
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document.write( "x = (-6 - square root((-6)^2 -4*3*(-4))) / (2(3)) = (-3 - square root(21)) / 3<BR>\n" );
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document.write( "c) y intercept is -4<BR>\n" );
document.write( "x intercepts are (-3 + square root(21)) /3, (-3 - square root(21)) / 3<BR>\n" );
document.write( "note the intercepts are where the graph of f(x) crosses the y axis(y intercept) and where f(x) crosses the x axis (x intercepts<BR>\n" );
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document.write( "d) The domain and range of f(x) are the real numbers<BR>\n" );
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document.write( "e) The graph of f(x) shows us the f(x) is increasing on the interval [-1, +infinity) and f(x) is decreasing on the interval [-infinity, -1]<BR>\n" );
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document.write( "f) see graph above<BR>\n" );
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