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lisabon 2012 [21]
3 years ago
14

Find the vertex I’d this parabola y=-2x^2-4x+4

Mathematics
1 answer:
mamaluj [8]3 years ago
5 0

Answer:

  (-1, 6)

Step-by-step explanation:

A graphing calculator shows the vertex to be (x, y) = (-1, 6).

__

You can also find it by putting the equation into vertex form.

  y = -2(x^2 +2x) +4

  y = -2(x^2 +2x +1) +4 +2(1) . . . . . add 1 inside parens; the opposite outside

  y = -2(x +1)^2 +6

Compare to ...

  y = a(x -h)^2 +k

and you see a=-2, h=-1, k=6

The vertex is (h, k) = (-1, 6).

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Answer:

29.4 cm

Step-by-step explanation:

The length of the space diagonal can be found to be the root of the squares of the three orthogonal edge lengths. For a cube, those edge lengths are all the same, so the diagonal length is ...

d = √(17^2 + 17^2 +17^2) = 17√3 ≈ 29.4 . . . . cm

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Consider a rectangular prism with edge lengths a, b, c. Then the face diagonal of the face perpendicular to edge "a" has length ...

(face diagonal)^2 = (b^2 +c^2)

and the space diagonal has length ...

(space diagonal)^2 = a^2 + (face diagonal)^2 = a^2 +b^2 +c^2

So, the length of the space diagonal is ...

space diagonal = √(a^2 +b^2 +c^2)

when the prism is a cube, these are all the same (a=b=c). This is the formula we used above.

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Step-by-step explanation:

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