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i have been stuck on this problem for days can someone please help me.use
\n" ); document.write( "completing the square to describe the graph f(x)=40-12x-x^2.support your answer graphically.\r
\n" ); document.write( "\n" ); document.write( " First review what a perfect square is. It is a trinomial which can be obtained by squaring a binomial( multiplying a binomial by itself.\r
\n" ); document.write( "\n" ); document.write( " For example a binomial has 2 terms. 2x^2 + 2x
\n" ); document.write( " or 4x + 5
\n" ); document.write( " When you have a trinomial with an x^2 term and
\n" ); document.write( " one x term
\n" ); document.write( " and one constant(number)
\n" ); document.write( " then the kind of binomial we
\n" ); document.write( " are looking to square is of the
\n" ); document.write( " form bx + c.\r
\n" ); document.write( "\n" ); document.write( " Let's square some binomials.\r
\n" ); document.write( "\n" ); document.write( " a) (x + 2) ^2 is (x + 2)(x + 2) = x ^2 + 4x + 4\r
\n" ); document.write( "\n" ); document.write( " b) (x + 3 ) ^2 = (x + 3)(x + 3) = x ^2 + 6x + 9
\n" ); document.write( " c) (x + 4) ^2 = (x + 4)(x +4) = x^2 + 8x +16
\n" ); document.write( " d) AND (x + 5) ^ 2 = (x+5)(x+5) = x^2 +10x + 25\r
\n" ); document.write( "\n" ); document.write( " I'm sensing a pattern.\r
\n" ); document.write( "\n" ); document.write( " a) 2(2) =4, 2^ 2 =4
\n" ); document.write( " b) 3(2) = 6, 3^2 =9
\n" ); document.write( " c) 4(2) =8 , 4^2 =8
\n" ); document.write( " d) 5(2 = 10, 5^2 =25\r
\n" ); document.write( "\n" ); document.write( " Now practice squaring binomials without writing each one twice as aabove.\r
\n" ); document.write( "\n" ); document.write( " (x + 6)^2 = X^2 + ___x + ___
\n" ); document.write( "
\n" ); document.write( "For the x coefficient, double the 6.
\n" ); document.write( "For the constant term, square the 6\r
\n" ); document.write( "\n" ); document.write( " so (x + 6) ^ 2 = x^2 + 12x + 36\r
\n" ); document.write( "\n" ); document.write( " x^2 +12x + ? to make a perfect square?
\n" ); document.write( " Take 1/2 of 12 and square it . 6^2 = 36.
\n" ); document.write( " Make this binomial into a perfect square.
\n" ); document.write( " x^2+ 16x + ? ( 1/2 of 16 = 8. 8^2 =64)
\n" ); document.write( " x^2 +16x + 64\r
\n" ); document.write( "\n" ); document.write( " We cannot have a - in front of the x, because squaring a number
\n" ); document.write( " never produces a negative.\r
\n" ); document.write( "\n" ); document.write( " Write 40 -12x - x^2 in standard form as
\n" ); document.write( " A. -x^2 -12x + 40 = y(or f(x))
\n" ); document.write( " Next we replace y with 0.
\n" ); document.write( " Why? Because points with y coordinate = 0
\n" ); document.write( " are on the x-axis., giving us the
\n" ); document.write( " x-intercepts.
\n" ); document.write( " Once we know the position of the intercepts we
\n" ); document.write( " find the line of symmetry that is
\n" ); document.write( " halfway between these points.
\n" ); document.write( " A. -x^2 -12x +40 = 0
\n" ); document.write( " -x^2 -12x = -40 (Multiply by -1.
\n" ); document.write( " B. x^2 + 12x = +40
\n" ); document.write( " Now what do we add to left
\n" ); document.write( " side to complete the square?
\n" ); document.write( " We add 1/2(12) and square it, getting 36. Add to BOTH sides.
\n" ); document.write( " B. x^2 +12x +36 = 40 +36
\n" ); document.write( " (x + 6)^2 = 76. taking sq. roots:
\n" ); document.write( " x + 6 = sq. root of 76
\n" ); document.write( " x + 6 = 8.7 0r x + 6 = -8.7
\n" ); document.write( " x = 2.7 and x = -14.7
\n" ); document.write( " Intercepts are (2.7, 0) and ( -14.7, 0)
\n" ); document.write( " Line of symmetry is x = -6
\n" ); document.write( " The vertex is on this line .
\n" ); document.write( " The x-coordinate is -6, and y coordinate is f(-6) \n" ); document.write( "