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algol [13]
3 years ago
11

Identify the vertex, focus, and directrix of the graph. Which of the following equations represents the parabola in the graph?

Mathematics
1 answer:
antoniya [11.8K]3 years ago
5 0

Answer:

Equation: (x-2)^2=16(y-2)

Vertex: (2,2)

Directrix: y=-2

Focus: (2,6)

Step-by-step explanation:

<u>Standard Form of Vertical Parabola:</u>

  • Equation -> (x-h)^2=4p(y-k) where p\neq 0
  • Vertex -> (h,k)
  • Directrix -> y=k-p
  • Focus -> (h,k+p)

We know that our vertex is (h,k) -> (2,2), therefore, we can determine the value of p by selecting a point from the parabola as (x,y):

(x-h)^2=4p(y-k)

(x-2)^2=4p(y-2)

(6-2)^2=4p(3-2)

(4)^2=4p(1)

16=4p

4=p

<u>Therefore:</u>

  • Directrix -> y=k-p -> y=2-4 -> y=-2
  • Focus -> (h,k+p) -> (2,2+4) -> (2,6)

<u>Conclusion:</u>

  • Equation -> (x-2)^2=16(y-2)
  • Vertex -> (2,2)
  • Directrix -> y=-2
  • Focus -> (2,6)

Review the graph for a visual

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