Question

Y=-1(x+3)^2+4 y=(x-5)^2+4 y=-(x-2)^2+4 y=-(x-1)^2-1

Answer 1

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Answer 2

These are four different equations of parabolas in vertex form. Here's what each of them means:

1. Y=-1(x+3)^2+4: This is a downward-facing parabola with vertex at (-3, 4).

2. y=(x-5)^2+4: This is an upward-facing parabola with vertex at (5, 4).

3. y=-(x-2)^2+4: This is a downward-facing parabola with vertex at (2, 4).

4. y=-(x-1)^2-1: This is a downward-facing parabola with vertex at (1, -1).

In general, the vertex form of a parabola is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola and a determines the shape and orientation of the parabola.

For example, in equation (1), the vertex is (-3, 4) and a is -1, which means that the parabola is downward-facing and opens wider than the standard parabola. In equation (2), the vertex is (5, 4) and a is 1, which means that the parabola is upward-facing and opens as the standard parabola.