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loris [4]
2 years ago
9

Write 1/3 x^2 - 4x + 17 in vertex form

Mathematics
1 answer:
Svetradugi [14.3K]2 years ago
8 0

Answer:

f(x)=−4(x+ 41 ) 2 − 4 11

Explanation:

The given function is

f(x) = - 4 {x}^{2} - 2x - 3f(x)=−4x 2 −2x−3

To write the function is vertex form, we need to complete the square.

We first factor -4 to get:

f(x) = - 4 ({x}^{2} + \frac{1}{2} x) - 3f(x−4(x2 + 21 x)−3

Add and subtract the square of half the coefficient of x.

f(x) = - 4( {x}^{2} + \frac{1}{2} x + \frac{1}{16} ) - \frac{1}{4} - 3f(x)=−4(x 2 + 21 x+ 16 1 )− 41 −3

We factor the perfect square trinomial and simplify to get:

f(x) = - 4( {x + \frac{1}{4} )}^{2} - \frac{11}{4}f(x)=−4(x+ 41 ) 2 − 4 11

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You would need 12ml of water.

6 0
3 years ago
VX
zhenek [66]

Answer:

The vertical line test can be used to determine whether a graph represents a function. If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because a function has only one output value for each input value.

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Hope it help you

6 0
2 years ago
Write an equation of the line that passes through the point (–1, 4) with slope 2. A. y+1=−2(x−4) B. y+1=2(x−4) C. y−4=2(x+1) D.
In-s [12.5K]

Answer:

y-4=2\,(x+1)

which agrees with answer C in your list of possible answers.

Step-by-step explanation:

We can use the general point-slope form of a line of slope m and going through the point (x_0, y_0):

y-y_0=m(x-x_0)

which in our case, given the info on the slope (2) and the point (-1, 4) becomes:

y-y_0=m\,(x-x_0)\\y-4=2\,(x-(-1))\\y-4=2\,(x+1)

6 0
3 years ago
At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of mi
tangare [24]

Answer:

The price for a small glass of milk is $0.95, and the price for a breakfast taco is $1.15.

Step-by-step explanation:

Let the price of a taco be x and the price for a small glass of milk be y.

x + y = 2.1

2x + 3y = 5.15

Multiply the first equation by 2:

2x + 2y = 4.2

Subtract the new third equation from the second equation:

(2x + 3y) - (2x + 2y) = 5.15 - 4.2

y = 0.95

Hence, the price for a small glass of milk is $0.95.

Substitute y into the first equation.

x + 0.95 = 2.1

x = 1.15

Therefore, the price for a breakfast taco is $1.15.

Hope this helped!

3 0
2 years ago
Read 2 more answers
Brainliest if correct! Please explain how this is done!
Korvikt [17]

The value of csc C in fraction and in decimal form is as follows:

csc C  = 5 / 3

csc C = 1.66666666667

Using trigonometric ratio,

secant A = 1 / cos A = hypotenuse / adjacent

Therefore,

sec A = 5/3

sec A = 1 / cos A

cos A = adjacent / hypotenuse

cos A = 3 / 5

A = cos⁻¹ 0.6

A = 53.1301023542

Therefore,

∠A = 53°

∠B = 90°

∠C = 180 - 143 =  37°

cosec C = 1 / sin C = hypotenuse / opposite

cosec C = 5 / 3

learn more about trigonometry here: brainly.com/question/25942962?referrer=searchResults

5 0
2 years ago
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