Parabola with Focus (-5,0) & Vertex (-5,-4): Find Equation

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SUMMARY

The equation for the parabola with a focus at (-5,0) and a vertex at (-5,-4) is derived from the standard form of a vertical parabola. The correct equation is (x + 5)^2 = 16(y + 4), which simplifies to x^2 + 10x + 16y + 89 = 0. The discussion highlights the importance of identifying the vertex and focus to confirm the parabola's properties, emphasizing the need for completing the square to derive the equation accurately.

PREREQUISITES
  • Understanding of parabola properties, including vertex and focus.
  • Knowledge of completing the square in quadratic equations.
  • Familiarity with the standard form of a parabola's equation.
  • Basic algebraic manipulation skills.
NEXT STEPS
  • Study the derivation of the standard form of a parabola's equation.
  • Learn how to complete the square for quadratic equations.
  • Explore the geometric properties of parabolas, including directrix and latus rectum.
  • Practice solving problems involving the focus and vertex of parabolas.
USEFUL FOR

Students studying algebra, mathematics educators, and anyone interested in mastering the properties and equations of parabolas.

TonyC
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Fins an equation for the parabola with focus at (-5,0) and vertex at (-5,-4).

I have come up with:

x^2 + 10x + 16y + 89 = 0

How far off am I?
 
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TonyC said:
Fins an equation for the parabola with focus at (-5,0) and vertex at (-5,-4).

I have come up with:

x^2 + 10x + 16y + 89 = 0

How far off am I?

Can't you check for yourself?

Is it a parabola? (That's easy- there is an x2 term but no y2 term.)

What is the vertex? (Solve for y, then complete the square.)

What is the focus? (You will need to know the equation for the focus of a given parabola.)
 
That is what I am having trouble determining. Can you show me step by step how to check myself?
 

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