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| Math Central | Quandaries & Queries |
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Question from Anne, a student: How do you find the vertex of the function f(x)=-x squared+7x-6 |
Hi Anne,
I want to illustrate with the function f(x) = -x2 -5x + 9. The technique to use is to complete the square
f(x) = -x2 -5x + 9
= -(x2 +5x) + 9
= -(x2 +5x + 25/4) + 9 + 25/4
= -(x + 5/4)2 + 61/4
Thus the graph of -(x + 5/4)2 is a parabola with vertex at x = -5/4 and opening downwards. The addition of the term 61/4 moves the entire graph upwards a distance of 61/4 units but the shape of the graph remains the same, it is a parabola with vertex at x = -5/4 and opening downwards.
I hope this helps,
Penny
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