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The y-intercept of a parabola is 1, and its vertex is at (1,0). What function does the graph represent?OA. Rx) = (x - 1)2
OB. Rx) = (x + 1)2
OC. Rx) = -1(x - 1)
OD. Rx) = -1(x + 1)2
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Answers

Answer 1
Answer:

Considering it's y-intercept and vertex, the equation of the parabola is given by:

y = (x - 1)^2

What is the equation of a parabola given it’s vertex?

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)^2 + k

In which a is the leading coefficient.

In this problem, the vertex is (1,0), hence h = 1, k = 0 and:

y = a(x - 1)^2

The y-intercept is of 1, hence, when x = 0, y = 1, so:

y = a(x - 1)^2

1 = a(0 - 1)^2

a = 1

Hence, the equation is:

y = (x - 1)^2

More can be learned about the equation of a parabola at brainly.com/question/24737967
Answer 2
Answer:

Answer:

A

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

Here (h, k) = (1, 0) , thus

y = a(x - 1)² + 0

To find a substitute the coordinates of the y- intercept (0, 1) into the equation

1 = a(- 1)² = a , thus

a = 1

y = (x - 1)² → A

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Quadrilateral MBPV is similar to quadrilateral GKDF. BP = 78 mm, KD = 30 mm , and FD = 45 mm. What is VP? Enter your answer in the box □mm.

Answers

Answer:

  VP = 117 mm

Step-by-step explanation:

Corresponding sides of similar quadrilaterals are proportional.

  VP/FD = BP/KD

  VP = FD·BP/KD = (45 mm)·(78/30) . . . . multiply by FD; fill in the givens

  VP = 117 mm

Help help
Math math math math

Answers

Answer:

4000

Step-by-step explanation:

Find the radius;

20/2=10

Plug everything into the equation;

4/3 (3) (10)^3= 4000

Hope this helps:) Have a good day!

Answer:

4000

Step-by-step explanation:

hope this helps

Find the value of x that will make L||M

Answers

Answer:

x = 17

Step-by-step explanation:

When two lines are intersected by a transversal, the interior on the same side of the transversal are called co interior angles and they are supplementary.

6x + 8 + 4x + 2 = 180

6x + 4x + 8 + 2 = 180   {Combine like terms}

         10x + 10  = 180  {Subtract 10 from both side}

                 10x = 180 - 10

                 10x = 170  {Divide both sides by 10}

                    x = 170/10

x = 17

8/3+7/5a

Simplify your answer as much as possible.

Answers

Answer:

mixed number: 4 1/15

Exact: 61/15
I think the answer is 8/3 + 7a/5

Write in slope-intercept form with the given information

Answers

you have to use point slope form

point slope form: y - y1 = m(x - x1)

x1 and y1 are the x and y values of the given point

m is the slope

so, just plug in the numbers:

y-3 = -2(x + 8)

now solve to put into slope intercept form (y = mx + b)

y-3 = -2x - 16

ANSWER: y = -2x -13

Answer:

y=-2x-13

Step-by-step explanation:

I am not sure if these what they want.

y-b=m(x-a)

y-3=-2(x--8)

y-3=-2x-16

add 3 to each side

y=-2x-13

Use Lagrange multipliers to find the indicated extrema, assuming that x, and y are positive.Minimize f(x,y)=x2−10x+y2−14y+28; Constraint: x+y=14

Answers

Answer:

- The values of x and y that minimize the function, subject to the given constraint are 6 and 8 respectively.

- The minimum value of the function = -44

Step-by-step explanation:

The Lagrange multiploer method finds the optimum value of a multivariable function subjected to a given constraint

It replaces the function with a Lagrange equivalent which is

L(x, y) = F(x, y) - λ C(x, y)

where λ Is the lagrange multiplier which can be a function of x and y

F(x, y) = x² - 10x + y² - 14y + 28

C(x, y) = x + y - 14

L(x, y) = x² - 10x + y² - 14y + 28 - λ (x + y - 14)

We now take the partial derivatives of the Lagrange function with respect to x, y and λ respecrively. Then solving to obtain values of x, y and λ that correspond to the minimum of the function. Since the first partial derivatives are all equal to 0 at minimum point.

(∂L/∂x) = 2x - 10 - λ = 0 (eqn 1)

(∂L/∂y) = 2y - 14 - λ = 0 (eqn 2)

(∂L/∂λ) = x + y - 14 = 0 (eqn 3)

Equating eqn 1 and 2

2x - 10 - λ = 2y - 14 - λ

2x - 10 = 2y - 14

2y = 2x - 10 + 14

2y = 2x + 4

y = x + 2 (eqn *)

Substitute eqn ^ into eqn 3

x + y - 14 = 0

x + x + 2 - 14 = 0

2x - 12 = 0

2x = 12

x = 6

y = x + 2 = 6 + 2 = 8

2x - 10 - λ = 0

12 - 10 - λ = 0

λ = 2

The values of x and y that minimize the function are 6 and 8 respectively.

F(x, y) = x² - 10x + y² - 14y + 28

At minimum point, x = 6, y = 8

F(x, y) = 6² - 10(6) + 8² - 14(8) + 28 = 36 - 60 + 64 - 112 + 28 = -44

Hope this Helps!!!
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