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Multiple Choice
Which equation from choices matches the quadratic graph below.
A
h(x)=−3(x+3)2+3
B
h(x)=−31(x−3)2+3
C
h(x)=−3(x−3)2+3
D
h(x)=−31(x+3)2+3
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Verified step by step guidance
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: \(y = a(x - h)^2 + k\), where \((h, k)\) is the vertex. Substitute \(h = 3\) and \(k = 3\) into the equation to get \(y = a(x - 3)^2 + 3\).
Determine the value of \(a\) by using another point on the graph. For example, use the x-intercept near 0 or 6. Substitute the x-value and y = 0 into the equation and solve for \(a\).
Check the sign of \(a\). Since the parabola opens downward, \(a\) should be negative.
Write the final equation with the vertex form and the calculated value of \(a\), which should match one of the given choices.