Determine whether the graph of y = −2x^2 + 7x + 3 opens up or down and whether it has a maximum or minimum
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Determine whether the graph of y = −2x^2 + 7x + 3 opens up or down and whether it has a maximum or minimum

[From: ] [author: ] [Date: 11-06-10] [Hit: ]
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point.

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Because the coefficient on x^2 is negative (-2), the parabola opens downward, and therefore it has a maximum.

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y = −2x^2 + 7x + 3
-2(x^2-7/2 x)+3
-2(x^2-7/2 x+(7/4)^2)+3+2(7/4)^2
-2(x-7/4)^2+3+49/8
-2(x-7/4)^2+73/8
-2(x-7/4)^2+73/8

Parabola opens downward since the coefficient of x^2 < 0; the vertex is at the maximum
vertex is :(7/4,73/8)
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