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Vertex (3, -8), symmetric with respect to the line y = -8, and contains the point (5, -4)

User PseudoToad
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2 Answers

3 votes
The correct answer is -8
User Muichkine
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2 votes

Final answer:

The problem is about finding the equation of a parabola with a given vertex and a point it contains, considering the line of symmetry is horizontal y = -8.

Step-by-step explanation:

The student is dealing with a geometry problem that involves understanding the properties of a parabola. The question at hand describes a vertex of a parabola and a line of symmetry, which gives us clues to use for the formulation of the equation of the parabola. Given the vertex (3, -8) and symmetry with respect to the line y = -8, we infer that the parabola opens upward or downward. The additional point (5, -4) that lies on the parabola helps us determine the specific equation of the parabola. Since the symmetry line is horizontal, the parabola will have an equation that follows the format y = a(x - h)² + k, where (h, k) is the vertex. Using the point (5, -4), we can substitute these values into the equation to solve for the coefficient a, which dictates the parabola's width and direction of opening.

User Erkan
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