Evaluate the vertical parabola
(y-2)2 = 12(x-5)
Open Direction
Since our squared variable is y, our parabola has a horizontal opening.
Determine the vertex (h,k):
Our standard for for this parabola is (y - k)2 = 4c(x - h)
Therefore, our vertex (h,k) = (5,2)
Determine focus:
From the right side of our standard form equation, we have 4c = 12
Divide each side by 4 to isolate c:
| 4c | |
| 4 |
| = |
| 12 |
| 4 |
c = 3
The focus for a horizontal parabola is (h + c,k)
Substituting our values into this equation, we get:
Focus = (5 + 3,2)
Focus = (8,2)
Calculate the directrix:
The directrix equation for a horizontal parabola is x = c
Therefore, for c = 3, we have x = 3
Common Core State Standards In This Lesson
HSG.GPE.A.2
How does the Parabolas Calculator work?
Free Parabolas Calculator - Determines the focus, directrix, and other related items for a parabola.
This calculator has 1 input.
This calculator has 1 input.
What 5 formulas are used for the Parabolas Calculator?
standard horizontal parabola equation is y2 = 4cx
standard vertical parabola equation is x2 = 4cy
If the x coefficient is negative, then parabola opens left
If the x coefficient is positive, then parabola opens right
standard vertical parabola equation is x2 = 4cy
If the x coefficient is negative, then parabola opens left
If the x coefficient is positive, then parabola opens right
What 4 concepts are covered in the Parabolas Calculator?
- directrix
- line in a parabola not through the focus
- focus
- fixed point on the interior of a parabola used in the formal definition of the curve
- parabola
- a plane curve which is approximately U-shaped
- parabolas
