To determine the vertex form of the equation of an upward-opening parabola, we use the formula:
\[ y = a(x - h)^2 + k \]
In this formula, \((h, k)\) represents the vertex of the parabola.
Since I do not have access to the image you mentioned, I cannot see the exact coordinates of the vertex or the value of \(a\). However, you should be able to identify the vertex from the graph of the parabola. Look for the point where the parabola changes direction; this will be the vertex \((h, k)\).
Once you locate the vertex:
- Identify the \(x\)-coordinate of the vertex (this will be \(h\)).
- Identify the \(y\)-coordinate of the vertex (this will be \(k\)).
- Determine the value of \(a\): since the parabola opens upward, \(a\) will be positive. You could estimate \(a\) based on another point on the parabola if available, using the form \(y = a(x - h)^2 + k\) to solve for \(a\).
Once you have \(h\), \(k\), and \(a\), you can write the vertex form of the equation.
For example, if the vertex was at point (3, 2) and \(a\) was determined to be 1, then the equation would be:
\[ y = 1(x - 3)^2 + 2 \] which simplifies to \[ y = (x - 3)^2 + 2 \]
Please fill in the specific values based on the graph you're analyzing.
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