All categories

3 years ago

What is the equation of the quadratic graph with a focus of (3, 1) and a directrix of y = 5?

Mathematics

1 answer:

mamaluj [8]3 years ago

3 0

Answer:

y = -⅛(x - 3)² + 3

Step-by-step explanation:

(x - h)² = 4p(y - k)

h = 3

k + p = 1

k - p = 5

2k = 6

k = 3

p = -2

(x - 3)² = 4(-2)(y - 3)

(x - 3)² = -8(y - 3)

y = -⅛(x - 3)² + 3

You might be interested in

Joey has 8 pairs of socks in his drawers five of them are white what percent of colored socks does he have

Vedmedyk [2.9K]

Answer: 62.5%

Step-by-step explanation:

first, set up the proportion. 5/8 = ?/100 in order to solve, divide 100 by 8.

the answer is 12.5. next you multiply it by 5 to get 62.5. fill it in to your equation, and you get 5/8 = 62.5/100. turn the second fraction into a percent, then you have your answer. 62.5%

3 0

2 years ago

the average mark of three pupils are 68. what is the ratio of 5:4:3. how many marks did the best student get? HELP ME!

noname [10]

Answer:

85, 68, 51

Step-by-step explanation:

Average: The sum of all the numbers divided by the number of numbers

If the ratio of the scores is 5 : 4 : 3, let's just set it as 5x : 4x : 3x

Then using the definition of an average, we can write this equation.

(5x + 4x + 3x) / 3 = 68

Multiply both sides by 3.

5x + 4x + 3x = 68 * 3

Simplify.

12x = 204

x = 17

Now, substitute x = 17 into the original scores (5x, 4x, and 3x)

5x = 5 * 17 = 85

4x = 4 * 17 = 68

3x = 3 * 17 = 51

Just in case, let's check this answer. Find the average of the 3 test scores.

(85 + 68 + 51) / 3 =

204 / 3 = 68

Thus, the answers are correct

3 0

3 years ago

Cierra has 3 more than one half as many purses as Aisha define the variable and write an expression to represent the number of p

77julia77 [94]

Cierra has 9 purses..

4 0

2 years ago

A frosting is made of cream cheese and powdered sugar in the ratio 3:2. If you use 120g or cream cheese, how much powdered sugar

siniylev [52]

Answer: 80 g

Step-by-step explanation:

Given

The frosting is made of cream cheese and Powdered sugar in the ratio of 3:2.

If 120 g of cheese is used

Assume the quantity of powdered sugar is x

So, we can write the ratio as

$\Rightarrow \dfrac{3}{2}=\dfrac{120}{x}\\\\\Rightarrow x=\dfrac{2}{3}\times 120\\\\\Rightarrow x=\dfrac{2}{3}\times 3\times 40\\\\\Rightarrow x=80\ g$

So, 80 g of powdered sugar is used.

3 0

3 years ago

Read 2 more answers

How many more unit tiles must be added to the function f(x)=x2−6x+1 in order to complete the square?

Valentin [98]

<h2>8 unit tiles should be added</h2>

Step-by-step explanation:

Function given is $f(x)=x^{2}-6x+1$ . We wish to add more unit tiles to the function so that it becomes a complete square.

Since the given function is of order 2, the side of the square will be order 1. Let us assume a general order 1 expression $ax+b$ to be the side of the square.

As the function forms the square after adding some $p$ unit tiles, $f(x)+p=(\text{Side of square})^{2}$

$x^{2}-6x+1+p=(ax+b)^{2}=a^{2}x^{2} +2abx+b^{2}$

From comparision, $a^{2}=1; 2ab=-6; b^{2}=1+p\\a=1; b=-3\\(-3)^{2}=p+1\\p=8$

∴ 8 more unit tiles are required to complete the square.

10 0

3 years ago

Read 2 more answers