The equation of a parabola is given.y=1/8x^2+4x+20 What are the coordinates of the focus of the parabola?

2 answers:

8 0

He equation of a parabola is x = -4(y-1)^2. What is the equation of the directrix?
You may write the equation as 
(y-1)^2 = (1) (x+4) 
(y-k)^2 = 4p(x-h), where (h,k) is the vertex 
4p=1 
p=1/4 
k=1 
h=-4 

The directrix is a vertical line x= h-p 
x = -4-1/4 
x=-17/4 

------------------------------- 
What is the focal length of the parabola with equation y - 4 = 1/8x^2 
(x-0)^2 = 8(y-4) 
The vertex is (0,4) 
4p=8 
p=2 (focal length) -- distance between vertex and the focus 
------------------------------- 
(y-0)^2 = (4/3) (x-7) 
vertex = (7,0) 
4p=4/3 
p=1/3 
focus : (h+p,k) 
(7+1/3, 0)

Romashka-Z-Leto [24]4 years ago

4 0

Convert it to vertex form we get

y = 1/8(x + 16)^2 - 12

so the vertex is at (-16,-12) and the x coordinate of the focus will be -16)

The focus will be at (-16, k + p) Here k = -12 from the vertex equation and p = 1 / 4a where a = 1/8 so p = 1 / 1/2 = 2 So k + p = -12 + 2 = -10

So the coordinates of the focus are (-16, -10) answer

You might be interested in

A bakery finds that the price they can sell cakes is given by the function p = 580 − 10x where x is the number of cakes sold per

dexar [7]

Answer:

The total revenue is $TR=580x-10x^2$ .

The marginal revenue is $MR=580-20x$ .

The fixed cost is $900.

The marginal cost function is $MC=50x+300$ .

Step-by-step explanation:

The Total Revenue ( $TR$ ) received from the sale of $x$ goods at price $p$ is given by

$TR=p\cdot x$

The Marginal Revenue ( $MR$ ) is the derivative of total revenue with respect to demand and is given by

$MR=\frac{d(TR)}{dx}$

From the information given we know that the price they can sell cakes is given by the function $p=580-10x$ , where $x$ is the number of cakes sold per day.

So, the total revenue is

$TR=(580-10x)\cdot x\\TR=580x-10x^2$

And the marginal revenue is

$MR=\frac{d}{dx}(580x-10x^2) \\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\MR=\frac{d}{dx}\left(580x\right)-\frac{d}{dx}\left(10x^2\right)\\\\MR=580-20x$

The Fixed Cost ( $FC$ ) is the amount of money you have to spend regardless of how many items you produce.

The Marginal Cost ( $MC$ ) function is the derivative of the cost function and is given by

$MC=\frac{d(TC)}{dx}$

We know that the total cost function of the company is given by $C=(30+5x)^2$ , which it is equal to

$\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a+b\right)^2=a^2+2ab+b^2\\a=30,\:\:b=5x\\\\\left(30+5x\right)^2=30^2+2\cdot \:30\cdot \:5x+\left(5x\right)^2=25x^2+300x+900\\\\C=25x^2+300x+900$

From the total cost function and applying the definition of fixed cost, the fixed cost is $900.

And the marginal cost function is

$MC=\frac{d}{\:dx}\left(25x^2+300x+900\right)\\\\MC=\frac{d}{dx}\left(25x^2\right)+\frac{d}{dx}\left(300x\right)+\frac{d}{dx}\left(900\right)\\\\MC=50x+300+0=50x+300$