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3 years ago

What is y=2x^2-12x+16 in vertex form

Mathematics

1 answer:

Natasha2012 [34]3 years ago

3 0

Answer:

y = 2(x-3)^2 - 2

Step-by-step explanation:

y = 2x^2 - 12x + 16

y = 2(x^2 - 6x + 8)

y = 2(x^2 - 6x +8 +1 -1) you "complete the square" by bringing the last term (8) up to "half of the middle co-efficient squared". Middle co-efficient is -6, half is -3, squared is 9. To get from 8 to 9 you must add 1 (+1), but if you add 1 you must subtract 1 (-1) so that you don't change the overall value of inside the bracket

y = 2(x^2 - 6x +9) - 2 (bring the -1 outside of the brackets)

y = 2(x-3)^2 - 2

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3 years ago

What are the x and y-intercepts of the line?

natta225 [31]

Answer:

Step-by-step explanation:

To find the y-intercept, plug in x=0 in the original equation. (You want to find what y is when x=0)

2x + 3y = -12

2(0) + 3y = -12 (Plug in x=0)

3y = -12 (2*0=0, so you can ignore that part)

y = -4 (Divide both sides by 3)

This narrows down our choices to either A or B.

To find the x-intercept, plug in y=0 into the original equation. (You want to find what x is when y=0)

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2x + 3(0) = -12 (Plug in y=0)

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4 years ago

A relay race is 1/10 kilometer long. Four athletes will run an equal distance to complete the relay. How far does each athlete r

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3 years ago

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Step-by-step explanation:

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3 years ago

If sin θ = 1/2 , then find the value of (sin 3 θ)/(1+ cos 2 θ)

Ipatiy [6.2K]

EXPLANATION:

Given that

sin θ = 1/2

We know that

sin 3θ = 3 sin θ - 4 sin³ θ

⇛sin 3θ = 3(1/2)-4(1/2)³

⇛sin 3θ = (3/2)-4(1/8)

⇛sin 3θ = (3/2)-(4/8)

⇛sin 3θ = (3/2)-(1/2)

⇛sin 3θ = (3-1)/2

⇛sin 3θ = 2/2

⇛sin 3θ = 1

and

cos 2θ = cos² θ - sin² θ

⇛cos 2θ = 1 - sin² θ - sin² θ

⇛cos 2θ = 1 - 2 sin² θ

Now,

cos 2θ = 1-2(1/2)²

⇛cos 2θ = 1-2(1/4)

⇛cos 2θ = 1-(2/4)

⇛cos 2θ = 1-(1/2)

⇛cos 2θ = (2-1)/2

⇛cos 2θ = 1/2

Now,

The value of sin 3θ /(1+cos 2θ

⇛1/{1+(1/2)}

⇛1/{(2+1)/2}

⇛1/(3/2)

⇛1×(2/3)

⇛(1×2)/3

⇛2/3

Answer : Hence, the req value of sin 3θ /(1+cos 2θ) is 2/3.

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