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Consider the function: \( f(x)=-x^{2}+12 x-32 \) The direction of the graph is like which of the following:

Ask by Barker Delgado. in the United States
Mar 14,2025

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The graph of the function opens downwards.

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Bonus Knowledge

This function is a quadratic equation of the form \( f(x) = ax^2 + bx + c \) where \( a = -1 \). Since the coefficient \( a \) is negative, the graph of this function is a downward-opening parabola. Picture a frown instead of a smile! To better understand this function, you could find its vertex. The vertex can tell you the maximum or minimum value of the function, which is a key feature of quadratics. The x-coordinate of the vertex is found using the formula \( -\frac{b}{2a} \). For this function, it's at \( x = 6 \) which gives you the peak of this frowning parabola!

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