Whats the value of a? =-=
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/A7e5M
The only thing I know is that:
1. Reflected in x-axis
2. vertical shift UP 2
Whats the vertical compression/stretch? halps~
This time I was able to see your graph,
the new vertex is (0,2) and another point on it is (1,-1)
so if the parent equation is y = x^2
the new equation is
y = a(x-0)^2 + 2
y = ax^2 + 2
but the point (1,-1) lies on it
1 = a(-1)^2 + 2
1 = a + 2
a = -1
new equation: y = -x^2 + 2
Notice that because of the position of the new point (1,-1) the value of a turned out be negative, which we expected, since it opens downwards
Thank you Reiny!!!!!!!
To determine the equation of the function in the form y=a(x-h)^2+k, we need to find the values of a, h, and k.
From the given information, we know that the graph is a reflection of the graph y=x^2 in the x-axis and has a vertical shift upward by 2 units.
1. Reflection in the x-axis: When a graph is reflected in the x-axis, this means that the signs of the y-coordinates are flipped. In this case, since the graph is a reflection of y=x^2, the equation becomes y=-x^2.
2. Vertical shift upward by 2 units: To shift a graph vertically, we add or subtract a constant value to the equation. In this case, the graph was shifted upward by 2 units, so the equation changes to y=-(x^2) + 2.
Now, let's focus on finding the value of a, which represents the vertical compression/stretch.
To determine the vertical compression/stretch, we need to examine the shape of the graph. However, since the given graph is only described as a reflection and a vertical shift, we don't have enough information to determine the vertical compression/stretch.
To find the value of a, we would need to know either the vertical stretch factor (if the graph is stretched vertically) or the vertical compression factor (if the graph is compressed vertically). Without this information, it is not possible to determine the exact value of a.
However, if you have any additional information about the graph or if you are able to provide specific points on the graph, we can further analyze and determine the value of a.