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For a quadratic with a vertex of (4, 1) with the graph opening downward, is this the right construction in vertex form?

-a(x - 4) + 1

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It's good. You don't really need the leading "-" if you say a is negative, but having it there does signal your intentions clearly.

Actually, the assignment says the graphs opens downward and asks me to put in in the equation. So then this looks fine, right?

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