Questions: Which equation best matches the graph shown below? y=-(x-4)^2-3 y=-(x+4)^2+3 y=-(x-4)^2+3 y=-(x+4)^2-3

Transcript text: Which equation best matches the graph shown below? $y=-(x-4)^{2}-3$ $y=-(x+4)^{2}+3$ $y=-(x-4)^{2}+3$ $y=-(x+4)^{2}-3$

Solution

Solution Steps

Step 1: Identify the Vertex of the Parabola

The vertex of the parabola is at the point (4, -3).

Step 2: Determine the Direction of the Parabola

The parabola opens downwards, indicating a negative coefficient for the squared term.

Step 3: Write the Vertex Form of the Equation

The vertex form of a parabola is $ y = a(x - h)^2 + k $, where (h, k) is the vertex. Given the vertex (4, -3) and the downward opening, the equation is $ y = -(x - 4)^2 - 3 $.

Final Answer

\[ y = -(x - 4)^2 - 3 \]

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