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Multiple Choice
Which graph from choices matches the quadratic equation below.
A
A
B
B
C
C
D
D
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1
Identify the vertex form of the quadratic equation given: \(h(x) = -(x-3)^2 + 2\). The vertex form is \(h(x) = a(x-h)^2 + k\), where \((h, k)\) is the vertex of the parabola.
From the equation, determine the vertex: it is at \((3, 2)\) because \(h = 3\) and \(k = 2\).
Note the coefficient \(a = -1\), which means the parabola opens downward (since \(a\) is negative).
Look at the graphs and find the parabola with vertex at \((3, 2)\) and opening downward.
Compare the options and select the graph that matches these characteristics, which is the one labeled 'C'.