To determine the k-value for the vertical stretch from the original function (the solid parabola) to the dilated function (the dotted parabola), we would typically analyze the vertex form of the parabolas. The vertex form of a parabola can be expressed as:
\[ y = a(x - h)^2 + k \]
where \((h, k)\) is the vertex of the parabola, and \(a\) is the coefficient that determines the width and vertical stretch of the parabola.
-
Identify the vertex: Since both parabolas share a vertex, this will be the same point for both equations.
-
Determine the coefficients: Examine the two parabolas to see how wide or narrow each one is, based on the coefficient \(a\). The solid parabola (original function) will have a certain \(a\) value, say \(a_1\), while the dotted parabola (dilated function) will have a different \(a\) value, say \(a_2\).
-
Calculate the k-value: The k-value represents the vertical stretch factor, which can be calculated by taking the absolute value of the ratio of the coefficients:
\[ k = \frac{|a_2|}{|a_1|} \]
Without the visual representation of the parabolas, I can't provide a specific numeric answer. However, you can follow these steps with the given images to find the k-value. If you can provide the specific heights or widths described by each function, I can help you derive the k-value directly.
1 answer