Question

Please help:

write a rule for g described by the transformations of the graph of f. Then identify the vertex.
1. f(x) = x²; vertical stretch by a factor of 5 and a reflection in the x-axis, followed by a translation 3 units down

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Answer 1

Rule for g after transformations is g(x) = -5x² - 3, with a vertex at (0, -3). These transformations include a vertical stretch, reflection in the x-axis, and translation downwards.

Step-by-step explanation:

To write a rule for g described by the transformations of the graph of f(x) = x² with a vertical stretch by a factor of 5 and a reflection in the x-axis, followed by a translation 3 units down, we enact the following steps:

1. Apply the vertical stretch by multiplying the function by 5, resulting in 5x².
2. Reflect the graph over the x-axis by multiplying the entire function by -1, giving us -5x².
3. Translate the graph 3 units down by subtracting 3, resulting in g(x) = -5x² - 3.

The vertex of the original function f(x) = x² is (0,0). The transformations do not affect the x-coordinate of the vertex but will change the y-coordinate. After the stretch, reflection, and translation, the vertex of g is (0, -3).