How to find the equation of a parabola with the following vertex.

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To find the equation of a parabola with a vertex at (-3, -2) that opens downward, the standard form is y = a(x + 3)² - 2, where 'a' is negative. The initial attempt of y = -3x² - 3x - 2 was incorrect. The correct approach involves using the vertex form and ensuring 'a' is a negative value to achieve the downward opening. The discussion emphasizes the importance of correctly identifying the vertex and the sign of 'a' in the equation. Understanding this will help in accurately determining the parabola's equation.
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1. I need to find the equation of a parabola with a vertex of (-3,-2). It has to open down.



2. I understand of hopefully will understand it.



3. My answer was y=-3x Squared -3x-2 Which I found to be wrong.

 
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Hi Cobalt! Welcome to PF! :smile:
Cobalt said:
1. I need to find the equation of a parabola with a vertex of (-3,-2). It has to open down.
…
My answer was y=-3x Squared -3x-2 Which I found to be wrong.

yes, it goes through (-3,-2) …

but it's -3(x + 0.5)2 + something. :wink:
 
A parabola with vertex at (x0, y0) is given by
y= a(x- x0)2+ y0. If opens downward, then a must be negative.
 

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