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Asked Nov 19, 2019
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2y
46 0
13-20 Graphing Shifted Parabolas An equation of a parabola
is given. (a) Find the vertex, focus, and directrix of the parabola.
(b) Sketch a graph showing the parabola and its directrix
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2y 46 0 13-20 Graphing Shifted Parabolas An equation of a parabola is given. (a) Find the vertex, focus, and directrix of the parabola. (b) Sketch a graph showing the parabola and its directrix

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Step 1
  1. a) Given equation of parabola is

The standard equation of a right-left parabola with vertex at (h,k) and focal length p is given by:

Rewriting the given equation:

Here h = 3, k = -1 and p = 4

Hence the vertex is (h,k) = (3, -1)

And the focus is given by (h + p, k) = (3 + 4, -1) = (7,-1)

The directrix is given by x = hp

Hence, the directrix is x = 3 – 4 = -1

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(y+1)16(x-3) (y-k)4p(x-h) (y-(-) = 4(4) (x-3)

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Step 2

b)

Plotting the graph using the ...

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5 X-1 4 3 2 1 -4 -2 -1 0 2 5 -1 -2 -3 -4 -5

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Math

Calculus