Question 92417
Given:
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{{{f(x)=-3*(x)^2 + 2x + k}}}
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Substitute y for f(x) to convert the given equation to the equivalent form:
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{{{y=-3*(x)^2 + 2x + k}}}
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You are told that the point (-1,3) is on the graph.  That means that when x is -1, the corresponding
value of y is 3. So you can substitute -1 for x and 3 for y and the equation should still
be true.  Make these two substitutions and the equation becomes:
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{{{3=-3*(-1)^2 + 2(-1) + k}}}
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Square the minus one on the right side to get -1*-1 = +1 and the equation becomes:
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{{{3=-3*(1) + 2(-1) + k}}}
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Multiply the first two terms on the right side and you get:
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{{{3=-3 -2 + k}}}
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Combine the first two terms on the right side and the result is:
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{{{3 = -5 + k}}}
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Get rid of the -5 on the right side by adding +5 to cancel it out.  But if you add +5
to the right side, you must also add +5 to the left side.  Adding +5 to both sides gives
you:
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{{{8 = k}}}
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and that's your answer.
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You can check this by replacing k by +8 in the original equation to get:
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{{{f(x) = -3x^2 + 2x + 8}}}
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Then let x = -1 and see if the left side is +3 as the problem said that y should be +3
when x is -1.
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Hope this helps you to see your way through this problem.
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