Using transformation concepts, it is found that:
- The rule for g is: [tex]g(x) = -4x^2[/tex]
- The vertex is: (0,0).
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- Stretching a function [tex]f(x)[/tex] vertically by a factor of b is given by: [tex]g(x) = bf(x)[/tex]
- Reflecting a function over the x-axis is the equivalent of: [tex]g(x) = -f(x)[/tex]
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- The original function is: [tex]f(x) = x^2[/tex].
- Stretching by a factor of 4 means that the function is multiplied by 4, thus: [tex]g(x) = 4x^2[/tex]
- Reflecting over the x-axis, that is, multiplying by -1, we have that: [tex]g(x) = -4x^2[/tex], which is the rule for g.
- From the graph added at the end of this answer, the vertex is at (0,0).
A similar problem is given at https://brainly.com/question/15196246
