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Dvinal [7]
3 years ago
10

Y=2x^2+12x+14 in vertex form

Mathematics
1 answer:
balandron [24]3 years ago
4 0

Answer:

y = 2(x + 3)² - 4

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Using the method of completing the square

y = 2x² + 12x + 14 ← factor out 2 from the first 2 terms

  = 2(x² + 6x) + 14

To complete the square

add/subtract ( half the coefficient of the x- term)² to x² + 6x

y = 2(x² + 2(3)x + 9 - 9 ) + 14

  = 2(x + 3)² - 18 + 14

  = 2(x + 3)² - 4 ← in vertex form

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For the rhombus below, find the measure of angles 1,2,3 and 4.
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Answer:

∠1 is 33°

∠2 is 57°

∠3 is 57°

∠4 is 33°

Step-by-step explanation:

First off, we already know that ∠2 is 57° because of alternate interior angles.

Second, it's important to know that rhombus' diagonals bisect each other; meaning they form 90° angles in the intersection. Another cool thing is that the diagonals bisect the existing angles in the rhombus. Therefore, 57° is just half of something.

Then, you basically just do some other pain-in-the-butt things after.

Since that ∠2 is just the bisected half from one existing angle, that means that ∠3 is just the other half; meaning that ∠3 is 57°, as well.

Next is to just find the missing angle ∠1. Since we already know ∠3 is 57°, we can just add that to the 90° that the diagonals formed at the intersection.

57° + 90° = 147°

180° - 147° = 33°

∠1 is 33°

Finally, since that ∠4 is just an alternate interior angle of ∠1, ∠4 is 33°, too.

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