How do I find the vertical/horizontal compression/stretch?
For the graph, determine the equation of the function in the form y=a(x-h)^2+k. Then describe the transformations that were applied to y=x^2 to obtain the graph.
Here is the graph:
imgur dot com/ft6lA
I got reflected in x-axis and vertical shift by 2 (UP 2)
However, I don't know how to find the vertical/horizontal compression/stretch?
I cannot access your new picture, but it might help you to look at the post reply I just added to your previous problem.
Perhaps you can use it to answer this question.
I tried looking through previous post but i don't understand it
To determine the vertical/horizontal compression or stretch, you need to take a closer look at the equation of the function in vertex form, which is y = a(x-h)^2 + k.
Vertical Compression/Stretch:
The value of "a" in the equation determines the vertical compression or stretch of the graph. If the absolute value of "a" is greater than 1, it indicates vertical compression, meaning the graph is narrower than the standard parabola (y = x^2). If the absolute value of "a" is less than 1, it indicates vertical stretch, meaning the graph is wider than the standard parabola. If "a" equals 1, there is no vertical compression or stretch.
Horizontal Compression/Stretch:
The horizontal compression or stretch can be determined by analyzing the coefficient of the x-term in the equation, (x-h)^2. In the vertex form, the coefficient of the x-term is always 1. So, if there is no coefficient other than 1, it means there is no horizontal compression or stretch.
To determine the values of a, h, and k in the given equation, y=a(x-h)^2+k, from the graph you provided, follow these steps:
1. Identify the vertex: The vertex is the intersection point of the parabola and the axis of symmetry. In this case, the vertex appears to be (2, -2).
2. Identify the vertical translation (k): The value of k is the y-coordinate of the vertex. Since the vertex is (2, -2), k = -2.
3. Identify the vertical reflection: If the graph is reflected in the x-axis, it means a negative sign is applied to the entire equation, so a = -1.
4. Plug in the values: Using the identified values, we now have y = -1(x-2)^2 - 2. This equation represents the function that matches the given graph.
Based on this equation, you can conclude that the graph represents a parabola that is reflected in the x-axis, shifted 2 units upward, and does not have any vertical or horizontal compression or stretch (since a = -1 and the coefficient of x is 1).