The function g (x) = - x2 + 16x - 44 written in vertex form is g (x) = - (x - 8) 2 + 20. Which is one of the transformations applied to the graph of f (x) = x2 to change it into the graph of g (x) = - x2 + 16x - 44?

The graph of f (x) = x2 is widened.

The graph of f (x) = x2 is shifted left 8 units.

The graph of f (x) = x2 is shifted down 44 units.

The graph of f (x) = x2 is reflected over the x-axis.

Question

Ariel Williams

Mathematics

5 January, 16:10

The function g (x) = - x2 + 16x - 44 written in vertex form is g (x) = - (x - 8) 2 + 20. Which is one of the transformations applied to the graph of f (x) = x2 to change it into the graph of g (x) = - x2 + 16x - 44?

The graph of f (x) = x2 is widened.

The graph of f (x) = x2 is shifted left 8 units.

The graph of f (x) = x2 is shifted down 44 units.

The graph of f (x) = x2 is reflected over the x-axis.

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Duarte · Answer 1

The graph of f (x) = x^2 is a parabola with vertex at the origin facing upwards. The graph of g (x) = - x^2 + 16x - 44 which is the same as the graph of - (x - 8) ^2 + 20 is a parabola with vertex at (8, 20) facing downwards. Therefore, to obtain the graph of g (x) = - x^2 + 16x - 44 from the graph of f (x) = x^2, we perform the series of transformations which include: The graph of f (x) = x^2 is shifted right 8 units; the graph of f (x) = x^2 is shifted up 20 units and the graph of f (x) = x^2 is refrected over the x-axis. Therefore, the correct answer to the question is "The graph of f (x) = x^2 is refrected over the x-axis".