Question

Describe the change in the graph of the parabola f(x) when it transforms into g(x) =

The parabola g(x) will open in the opposite direction of f(x), and the parabola will be narrower than f(x).
The parabola g(x) will open in the same direction of f(x), and the parabola will be narrower than f(x).
The parabola g(x) will open in the opposite direction of f(x), and the parabola will be wider than f(x).
The parabola g(x) will open in the same direction of f(x), and the parabola will be wider than f(x).

Answer 1

D.) The parabola g(x) will open in the same direction of f(x), and the parabola will be wider than f(x).

Explanation:

I got it right on the test :)

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Answer 2

(d) The parabola g(x) will open in the same direction of f(x), and the parabola will be wider than f(x).

Explanation:

We assume you intend ...

f(x) = equation of a parabola

g(x) = 2/3·f(x)

Multiplying a function by a factor of 2/3 will cause it to be compressed vertically to 2/3 of its original height. When the function is a parabola, this has the effect of making it appear wider than before the compression.

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The compression factor is positive, so points on the graph remain on the same side of the x-axis. The direction in which the graph opens is not changed.

The attachment shows parabolas that open upward and downward, along with the transformed version.