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Multiple Choice
Which equation from choices matches the quadratic graph below.
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1
Identify the vertex of the parabola from the graph. The vertex is the highest point since the parabola opens downward. From the graph, the vertex is at (3, 3).
Recall the vertex form of a quadratic equation: \(h(x) = a(x - h)^2 + k\), where \((h, k)\) is the vertex. Substitute the vertex coordinates into the equation to get \(h(x) = a(x - 3)^2 + 3\).
Determine the direction the parabola opens. Since it opens downward, the coefficient \(a\) must be negative.
Estimate the value of \(a\) by using another point on the graph. For example, use the point where \(x = 0\) and find the corresponding \(y\) value from the graph. Substitute \(x = 0\) and \(y\) into the vertex form equation and solve for \(a\).
Compare the value of \(a\) and the vertex form with the given choices to find the matching equation.