Question

Select the correct answer. A parabola declines through (negative 2, 4), (negative 1 point 5, 2), (negative 1, 1), (0, 0) and rises through (1, 1), (1 point 5, 2) and (2, 4) on the x y coordinate plane. The function f(x) = x2 is graphed above. Which of the graphs below represents the function g(x) = (x − 2)2 ? A parabola declines through (negative 4, 4), (negative 3, 1), (negative 2, 0) and rises through (negative 1, 1), (negative 0 point 5, 2) and (0, 4) on the x y coordinate plane. W. A parabola declines through (0, 4), (0 point 5, 2), (1, 1), (2, 0) and rises through (3, 1), (3 point 5, 2) and 4, 4) on the x y coordinate plane. X. A parabola declines through (negative 1 point 5, 4), (negative 1, 3), (0, 2) and rises through (1, 3), (1 point 5, 4) and (1 point 7, 5) on the x y coordinate plane. Y. A parabola declines through (negative 2 point 5, 4), (negative 2, 2), (negative 1 point 5, 0), (negative 1, negative 1), (0, negative 2) and rises through (1, negative 1), (2, 2) and (2 point 5, 4) on the x y coordinate plane. Z. W X Y Z

Answer 1

hw correct option based on the information given about the parabola will be B. X.

How to explain the parabola

The observed parabola has its vertex situated at (0, 0), declining until (0, 0) then again rising. Its equation falls in the form of f(x) = a(x - 0)² + 0, which simplifies to ax².

In order to detect the value of 'a' we can utilize any point on the parabola itself. Let's take (1, 1):

1 = a(1)²

1 = a

Therefore, the formula for the presented parabola is exsiting in the form of f(x) = x².

Now consider g(x) = (x + 1)² such that it's merely a horizontal movement of function f(x) = x². The vertex of g(x) stands at (-1, 0) and linearly declines until (-1, 1) prior to onching higher again. All this leaves us with option X as the only conceivable graph for g(x).

Therefore, the answer is B) X.

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