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You can put this solution on YOUR website!
if the vertex is (-2,-4), then the axis of symmetry would be x = -2.
\n" ); document.write( "if one of the x intercepts is 7, this means that the x value is 9 from the axis of symmetry.
\n" ); document.write( "this means that the other x intercept would be - 11.
\n" ); document.write( "this is because 7 - (-2) = 9
\n" ); document.write( "and:
\n" ); document.write( "-11 - (-2) = -9
\n" ); document.write( "which would make the equation symmetric about the axis of symmmetry.,
\n" ); document.write( "---
\n" ); document.write( "unfortunately, this leads to complications.
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\n" ); document.write( "if one of the roots of the equation is 7, and the other root of the equation is -11, this means that the equation is (x-7)*(x+11).
\n" ); document.write( "this would make the equation equal to x^2 + 4x - 77.
\n" ); document.write( "---
\n" ); document.write( "since the vertex is at (-2,-4), however, this yields to difficulty.
\n" ); document.write( "if x = -2, this equation yields y = 4 -8 - 77 = -81.
\n" ); document.write( "this is not consistent with the vertex being at (-2,-4).
\n" ); document.write( "it says the vertex is at (-2,-81)
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\n" ); document.write( "i suspect something wrong with the problem setup.
\n" ); document.write( "here's why.
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\n" ); document.write( "i can take any equation by multiplying by two roots.
\n" ); document.write( "take x = -7 as one of the roots.
\n" ); document.write( "take x = 3 as the other root.
\n" ); document.write( "my equation will be:
\n" ); document.write( "(x+7)*(x-3) = x^2 + 4x - 21.
\n" ); document.write( "---
\n" ); document.write( "the x coordinate of the vertex of this equation will be -b/2a = -4/2 = -2.
\n" ); document.write( "the y coordinate of the vertex of this equation will be f(-2) = 4 - 8 - 21 = -25
\n" ); document.write( "the vertex of this equation is therefore (-2,-29).
\n" ); document.write( "so far i have:
\n" ); document.write( "roots of this equation are:
\n" ); document.write( "x = -7
\n" ); document.write( "x = 3
\n" ); document.write( "and vertex of this equation is:
\n" ); document.write( "(-2,-25).
\n" ); document.write( "---
\n" ); document.write( "if somebody came to me and said:
\n" ); document.write( "the vertex of an equation is (-2,-25)
\n" ); document.write( "one of the x intercepts is -7
\n" ); document.write( "i would have no problem finding the other x intercept and the equation as follows:
\n" ); document.write( "i would say the axis of symmetry is x = -2 because the axis of symmetry of an equation that goes up and down is the x coordinate of the vertex.
\n" ); document.write( "i would then say that one of the x intercepts is -7.
\n" ); document.write( "this means that the distance from the x coordinate to the axis of symmetry is (-2) - (-7) = (-2) + 7 = 5.
\n" ); document.write( "to find the other x intercept i would simply add the 5 to the axis of symmetry going in the other direction and i would get (-2) + 5 = (3).
\n" ); document.write( "my other x intercept would be 3.
\n" ); document.write( "---
\n" ); document.write( "i would now have:
\n" ); document.write( "x = -7 (given)
\n" ); document.write( "vertex = (-2,-25) - again given.
\n" ); document.write( "x = 3 (calculated from the information given).
\n" ); document.write( "---
\n" ); document.write( "since i would now have both roots, i would be able to generate the equation.
\n" ); document.write( "(x+7) * (x-3) = x^2 + 4x - 21
\n" ); document.write( "---
\n" ); document.write( "there would be no conflict between the equation and the vertex of the equation.
\n" ); document.write( "---
\n" ); document.write( "in the problem that you stated above, there is a conflict which leads me to believe there is something wrong with the information being provided.
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\n" ); document.write( "i'm not a top expert at this and i would not say there is no solution.
\n" ); document.write( "i am only saying that i can't find one and that my thinking says there is a problem with the question.
\n" ); document.write( "---
\n" ); document.write( "here's a graph of the equation i just showed you would work based on the information i provided for it.
\n" ); document.write( "
\n" ); document.write( "note the x intercepts.
\n" ); document.write( "note the vertex.
\n" ); document.write( "they are in agreement with the information provided.
\n" ); document.write( "---
\n" ); document.write( "the next graph shows the information you provided and the equation i was able to calculate from it.
\n" ); document.write( "---
\n" ); document.write( "you gave the vertex as (-2,-4).
\n" ); document.write( "you gave one of the x intercepts at 7
\n" ); document.write( "i used that information to calculate the other x intercepts as -11.
\n" ); document.write( "i got (x-7)*(x+11) = x^2 + 4x - 77 as the equation based on the x intercepts.
\n" ); document.write( "the vertex of this equation is not the same as the vertex you provided.
\n" ); document.write( "the vertex i calculated from the equation is (-2,-81).
\n" ); document.write( "here's the graph of that equation.
\n" ); document.write( "
\n" ); document.write( "the problem is that the equation generated from the x intercepts does not provide the vertex given, but provides a different vertex, hence the conflict.
\n" ); document.write( "---
\n" ); document.write( "i suspect a problem with the problem setup.
\n" ); document.write( "if you find out different, i would be more than please to know.
\n" ); document.write( "i've beaten this to death and come up with the same answer every time.
\n" ); document.write( "---
\n" ); document.write( "that answer is that there seems to be a problem with the information provided in terms of the vertex and the x intercept. they do not appear to be compatible. \n" ); document.write( "