
To graph and describe translation of the function in relation to the graph of f(x)=x2 .

Explanation of Solution
Given information :
The function that is provided: g(x)=−15x2 .
Graph :
Interpretation :
The graph of a
This vertex point shall be:
Highest point (if a<0 ) and be called the maximum. Here, the graph opens downwards.
Or, lowest point (if a>0 ) and can be called the minimum. Here the graph opens upwards.
In this case, ‘a’ is lesser than 0 hence the graph will have a maximum and will open downwards.
A parabola always points to infinity, either negative or positive.
In the function g(x)=−15x2 , the value of a is negative and thus it opens downwards. Therefore, the transformation of the function with respect to the graph of f(x)=x2 , as seen in the graph shown above, is that the function has been inverted and now it open downwards.
The graph of quadratic function f(x) when multiplied by a positive constant a , the resulting graph af(x) is a vertical dilation of f(x) . The function is stretched or compressed vertically by a factor of |a| .
If |a| >1 , the graph of f(x) is stretched vertically, that is, all points on the graph f(x) move farther away from the x -axis.
If |a| <1 , the graph of f(x) is compressed vertically, that is, all points on the graph f(x) move closer to the x -axis.
In the function g(x)=−15x2 , the value of |a| <1 at a=15 . Thus, the transformation of f(x) when multiplied by a , as seen in the graph, is that it is compressed vertically by a factor of 15 .
Therefore, as seen in the graph, the transformation of the function with respect to the graph of f(x)=x2 is the inversion of the graph and vertical compression by a factor of 15 .
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