Questions: Graph the parabola. y=-2(x+6)^2-3

Graph the parabola. y=-2(x+6)^2-3
Transcript text: Graph the parabola. \[ y=-2(x+6)^{2}-3 \]
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Solution

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Solution Steps

Step 1: Identify the given equation

The given equation of the parabola is: \[ y = -2(x + 6)^{2} - 3 \]

Step 2: Determine the vertex of the parabola

The vertex form of a parabola is \( y = a(x - h)^2 + k \). Here, \( a = -2 \), \( h = -6 \), and \( k = -3 \). Therefore, the vertex is at \( (-6, -3) \).

Step 3: Determine the direction of the parabola

Since \( a = -2 \) is negative, the parabola opens downwards.

Final Answer

The equation of the parabola is: \[ y = -2(x + 6)^{2} - 3 \]

{"axisType": 3, "coordSystem": {"xmin": -12, "xmax": 0, "ymin": -20, "ymax": 5}, "commands": ["y = -2*(x + 6)**2 - 3"], "latex_expressions": ["$y = -2(x + 6)^{2} - 3$"]}

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