Question

What is the difference between g(x) = -x^2 and the parent function f(x) = x^2? Be specific and use complete sentences. 1) The graph of g(x) is a reflection of the graph of f(x) across the x-axis, resulting in a downward-facing parabola instead of an upward-facing one. 2) The vertex of g(x) is at the origin, while the vertex of f(x) is at (0,0). 3) The maximum value of f(x) is infinity, while the maximum value of g(x) is 0. 4) The y-intercepts of the two functions are different; f(x) has a y-intercept of 0, while g(x) has a y-intercept of (0,0).

Answer 1

The difference between g(x) = -x^2 and f(x) = x^2 is that g(x) is a reflection of f(x) with a downward-facing parabola, vertex at the origin, maximum value of 0, and a y-intercept of (0,0).

Step-by-step explanation:

The difference between the functions g(x) = -x^2 and f(x) = x^2 is as follows:

1. The graph of g(x) is a reflection of the graph of f(x) across the x-axis, resulting in a downward-facing parabola instead of an upward-facing one.
2. The vertex of g(x) is at the origin, while the vertex of f(x) is at (0,0).
3. The maximum value of f(x) is infinity, while the maximum value of g(x) is 0.
4. The y-intercepts of the two functions are different; f(x) has a y-intercept of 0, while g(x) has a y-intercept of (0,0).

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