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3 years ago

Rewrite the quadratic function in vertex form. Y=3x^2-12x+4

Mathematics

2 answers:

Shtirlitz [24]3 years ago

7 0

Answer:

y = 3(x - 2)² - 8

Step-by-step explanation:

The equation of a quadratic in vertex form is

y = a(x - h)² + k

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

To obtain this form use the method of completing the square

• The coefficient of the x² term must be 1

Factor out 3 from the first 2 terms

y = 3(x² - 4x ) + 4

• add/subtract (half the coefficient of the x- term )² to x² - 4x

y = 3(x² + 2(- 2)x + (- 2)² - (- 2)² ) + 4 ← complete the square

y = 3(x - 2)² - 12 + 4

y = 3(x - 2)² - 8 ← in vertex form

nataly862011 [7]3 years ago

6 0

Answer:

y=3(x-2)^2-8 I'm pretty sure

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Please answer question in picture below

Sonja [21]

9×7=63
63÷2=31.5
31.5×4=126

7×7=49

126+49=175

175 is the answer

8 0

3 years ago

(a) What is the actual cost incurred in producing the 1051st and the 2191st disc? (Round your answers to the nearest cent.)

Evgen [1.6K]

This question is incomplete, the complete question is;

The total weekly cost (in dollars) incurred by Lincoln Records in pressing x compact discs is given by the following function;

C(x) = 2000 + 2x -0.0001x² (0 ≤ x ≤ 6000) .

(a) What is the actual cost incurred in producing the 1051st and the 2191st disc? (Round your answers to the nearest cent.)

(b) What is the marginal cost when x = 1050 and 2190? (Round your answers to the nearest cent.)

Answer:

Actual cost for 1051st disc is $1.79

Actual cost for 2191st disc is $1.56

the marginal cost are;

C'(1050) = $1.79

C'(2190) = $1.56

Step-by-step explanation:

Given the data in the question;

C(x) = 2000 + 2x -0.0001x²

What is the actual cost incurred in producing the 1051st and the 2191st disc? (Round your answers to the nearest cent.)

Actual cost for 1051st disc will be;

⇒ C(1051) - C(1050)

= [ 2000 + 2(1051) - 0.0001×(1051)²] - [ 2000 + 2(1050) - 0.0001×(1050)² ]

= [ 2000 + 2102 - 110.4601 ] - [ 2000 + 2100 - 110.25 =

= 3991.5399 - 3989.75

= $ 1.7899 ≈ $1.79

Actual cost for 2191st disc will be;

⇒ C(2191) - C(2190)

= [ 2000 + 2(2191) - 0.0001×(2191)²] - [ 2000 + 2(2190) - 0.0001×(2190)² ]

= [ 2000 + 4382 - 480.0481 ] - [ 2000 + 4380 - 479.61 ]

= 5901.9519 - 5900.39

= $ 1.5619 ≈ $1.56

Therefore,

Actual cost for 1051st disc is $1.79

Actual cost for 2191st disc is $1.56

What is the marginal cost when x = 1050 and 2190? (Round your answers to the nearest cent.)

Marginal cost is; C'(x) = 2 - 0.0002x

so;

C'(1050) = 2 - 0.0002(1050) = 2 - 0.21 = $1.79

C'(2190) = 2 - 0.0002(2190) = 2 - 0.438 = $1.562 ≈ $1.56

Therefore; the marginal cost is;

C'(1050) = $1.79

C'(2190) = $1.56

3 0

3 years ago

If this is the graph of f(x) = a^(x+h) + k then

Natali [406]

Answer:

The domain is (-∞,∞) and range is (k,∞)

Step-by-step explanation:

The graph is given as $a^(x+h)+k$ .

When x =0, we have f(x) $a^h+k$ = y intercept

Consider the exponential function y = $a^x$ .

This is defined for domain all real numbers and range = (0,infinity) for all positive a.

This function is transformed into our function by horizontal shift of h units to left and vertical units of k units up.

i.e. Y = y-k and X = x-h

Since x has domain as set of all real numbers X also set of real numbers

So domain is (-∞,∞)

Since range of original graph is (0,∞), we have Y minimum value as k and max as infinity.

Range = (k,∞)

5 0

3 years ago

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If 8 is added to twice a number and this sum is multiplied by three, The result is the same as if the number is multiplied by fo

Harrizon [31]

Using the equation $3(2x + 8) = 4x + 10$ , I found out that x is equal to -7.
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$3(2x + 8) = 4x + 10$ - Written out equation
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$2x + 24 = 10$ - Subtracted 4x from both sides
$2x = -14$ - Subtraced 24 from both sides
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3 years ago