To determine the vertex form of the parabola given the point (2, -14), we can use the general form of a parabola's vertex equation, which is:
\[ y = a(x - h)^2 + k \]
where (h, k) is the vertex of the parabola. In this case, we need to identify the vertex (h, k) from the information given.
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Identifying the vertex: Since the parabola is upward-opening and given the point (2, -14) is on the graph, we can assume for a moment that point (2, -14) could potentially represent the vertex since it is a downward point on the y-axis. However, we need to confirm if this point is the vertex or not.
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Formulate the vertex: In vertex form, if the vertex is indeed at (h, k) = (2, -14), then we can express the equation as:
\[ y = a(x - 2)^2 - 14 \]
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Finding the value of a: To find the coefficient \( a \), we would typically need to know another point on the parabola, but since we don't have that data, we can leave it as a variable for growth and contraction of the parabola.
For the specific response format required, if we assume the vertex is indeed at (2, -14):
- Fill in \( h = 2 \) and \( k = -14 \):
The vertex form of the equation would be:
\[ y = (x - 2)^2 - 14 \]
So the answer is: y=(x−2)^2−14