To find the function for h(x), multiply 13 by the function f(x).
Describe the Transformation: The graph of h(x) is a vertical compression by a factor of 13 of the graph of f(x). Equation for h(x): h(x)=- 1/3(x+5)^2-2
Practice makes perfect
To describe the transformation, we need to identify the values of a, h, and k for h(x).
h(x)=1/3f(x)
⇕
h(x)= 1/3f(x- 0)+ 0
We can see above that a= 13, h= 0, and k= 0. Let's recall how to transform the graph of a quadratic function given these values.
f(x)=a(x-h)^2+k
h - Horizontal Translation
& h units right if h is positive
& |h| units left if h is negative
k - Vertical Translation
& k units up if k is positive
& |k| units down if k is negative
a - Orientation and Shape
If a<0, the graph is reflected across the x-axis
& If |a|>1, the graph is stretched vertically
& If 0<|a|<1, the graph is compressed vertically
Since h= 0 and k= 0, the graph of f(x) will not be translated horizontally or vertically. The value a= 13 represents a vertical compression by a factor of 13.
Equation for h(x)
In order to the find the function for h(x), mutiply 13 by f(x)=-(x+5)^2-6.
