The function g(x) = –3x2 – 36x – 60 written in vertex form is g(x) = –3(x + 6)2 + 48. Which is one of the transformations applie

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The function g(x) = –3x2 – 36x – 60 written in vertex form is g(x) = –3(x + 6)2 + 48. Which is one of the transformations applie

d to the graph of f(x) = x2 to change it into the graph of g(x) = –3x2 – 36x – 60? The graph of f(x) = x2 is made narrower. The graph of f(x) = x2 is shifted right 6 units. The graph of f(x) = x2 is shifted down 48 units. The graph of f(x) = x2 is reflected over the y-axis.

Mathematics

1 answer:

navik [9.2K] · Answer 1 · 2021-11-27T13:05:57+03:00

The vertex form of the function gives the vertex as (-6,48). The vertex of f(x)=x^2 is (0,0) so from this information, the vertex is moved LEFT 6 and UP 48. This cancels out two options. The coefficient -3 tells us that the graph is flipped or reflected over the x-axis (negative sign flips graph) and that all y-values will be 3 times as large. Larger y-values for the same x inputs makes the graph narrower.