To determine the vertex form of the equation of a parabola, we can use the general vertex form, which is given by:
\[ y = a(x - h)^2 + k \]
In this equation, \((h, k)\) is the vertex of the parabola.
Since I cannot see the image you referenced, I will guide you on how to find the vertex form of the parabola based on the graph. Here are the steps to determine the vertex:
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Identify the Vertex: Look at the graph to find the vertex of the parabola. It will be the point where the parabola changes direction (i.e., the minimum point for an upward-opening parabola).
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Read Coordinates: Once you've identified the vertex, note down the \(x\) and \(y\) coordinates of that point. Let's say the vertex is at the point \((h, k)\).
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Determine the Value of \(a\):
- Choose another point on the parabola from the graph (not the vertex) to determine the value of \(a\).
- Use the coordinates \((x_1, y_1)\) of that point in the equation to solve for \(a\): \[ y_1 = a(x_1 - h)^2 + k \]
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Construct the Equation: After determining \(a\), substitute \(h\), \(k\), and \(a\) back into the vertex form equation.
Please go ahead and identify the vertex and a point on the parabola using the instructions above, and then you can fill in the values into the vertex form of the equation.
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