To write the equation of the quadratic function in vertex form, \( y = a(x - h)^2 + k \), we need to identify the vertex \((h, k)\) of the parabola and the value of \( a \).
Given that the vertex form is already partially provided as \( y = 3(x - 1)^2 + _ \), it indicates that the vertex \( h \) is \( 1 \), and the coefficient \( a \) is \( 3 \).
Next, we need to determine the \( k \) value, which represents the y-coordinate of the vertex. Since you mentioned that the answer for \( k \) is not \( 2 \), we still need to find the actual y-coordinate of the vertex.
To find \( k \), we can observe the graph of the parabola. If the vertex of the parabola is located at \( (1, k) \), we can estimate \( k \) based on the point on the graph directly above or below the vertex at \( x = 1 \).
Without the graph image, I cannot directly identify the value of \( k \). However, if you have the graph, locate the y-value of the point at \( (1, k) \) on the curve to determine \( k \).
Please use that information to fill in the blank in the equation \( y = 3(x - 1)^2 + k \). If you order from the top of the y-axis, it would likely be a number between \( -1 \) and \( 6 \), excluding \( 2 \).