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

Therefore, the equation of the parabola is y= -3(x+3)2-2. In summary, the equation of the parabola with a vertex of (-3,-2) that opens down is y= -3(x+3)2-2.
  • #1
Cobalt
1
0
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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  • #2
Welcome to PF!

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:
 
  • #3
A parabola with vertex at (x0, y0) is given by
y= a(x- x0)2+ y0. If opens downward, then a must be negative.
 

What is a parabola?

A parabola is a type of curve that is represented by a quadratic equation. It is a symmetrical shape that resembles an arch, and can be found in various natural and man-made structures.

What is the vertex of a parabola?

The vertex of a parabola is the highest or lowest point on the curve, depending on whether the parabola opens upwards or downwards. It is also the point where the parabola changes direction.

What information do I need to find the equation of a parabola with a given vertex?

To find the equation of a parabola with a given vertex, you will need the coordinates of the vertex and at least one other point on the parabola. This could be either the x-intercept, y-intercept, or another point on the curve.

How do I find the equation of a parabola with a given vertex?

To find the equation of a parabola with a given vertex, you can use the standard form of a quadratic equation: y = a(x-h)^2 + k. The values of a, h, and k can be determined using the coordinates of the vertex and another point on the parabola.

What are some real-life applications of parabolas?

Parabolas have many practical applications, such as in architecture, engineering, physics, and astronomy. They are also used in the design of satellite dishes, suspension bridges, and parabolic reflectors in telescopes and solar panels.

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