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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 \(a = -1\) (the negative sign before the squared term), which means the parabola opens downward.
Look at the graphs and find the parabola with a vertex at \((3, 2)\) and that opens downward.
Compare the graphs and select the one that matches these characteristics, which is graph C.