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Mrac [35]
3 years ago
8

What is the equation of the quadratic graph with a focus of (3, 6) and a directrix of y = 4? f(x) = one fourth (x − 3)2 + 1 f(x)

= one fourth (x − 3)2 + 5 f(x) = −one fourth (x − 2)2 + 5 f(x) = −one fourth (x − 2)2
Mathematics
1 answer:
mina [271]3 years ago
8 0
 Let point (x, y) be any point on the graph, than the distance between (x, y) and the focus (3, 6) is sqrt((x - 3)^2 + (y - 6)^2) and the distance between (x, y) and the directrix, y = 4 is |y - 4|

Thus sqrt((x - 3)^2 + (y - 6)^2) = |y - 4|
(x - 3)^2 + (y - 6)^2 = (y - 4)^2
x^2 - 6x + 9 + y^2 - 12y + 36 = y^2 - 8y + 16
x^2 - 6x + 29 = -8y + 12y = 4y
(x - 3)^2 + 20 = 4y
y = 1/4(x - 3)^2 + 5

Required answer is f(x) = one fourth (x - 3)^2 + 5
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Sole the system by elimination -4x+9y=9 x-3y=-6
Natalka [10]

Answer:

A) -4x + 9y = 9

B) x -3y = -6

We multiply B) by 3

B) 3x -9y = -18 Then add it to A)

A) -4x + 9y = 9

-x = -9

x = 9

9 -3y = -6

3y = 15

y = 5


Step-by-step explanation:


5 0
2 years ago
Write a system of two equations in two variables to solve the problem. when fully extended, a ladder is 28 feet in length. if th
Alisiya [41]
Let the base of the ladder be x ft and the extension be y ft.

"when fully extended, a ladder is 28 feet in length."

means: x+y=28

"<span>the extension is 4 feet shorter than the base</span>"

means: y=x-4,   that is x-y = 4, (taking y to the side of x, and -4 to the other side of x and y)

thus, we have the system of equations:

1) x+y= 28 

2) x-y=4

adding the 2 equations, we have:

(x+y)+(x-y)=28+4

2x=32

x=32/2=16


x+y=28, so 16+y=28, thus y=12


Answer: Base: 16, Extension 12
5 0
2 years ago
I NEED HELPPP ASAP PLZZZZZZZZ everything except for 11,12,13, and 15 Please!!!!
n200080 [17]
14. 75     105
      105    75

16. 155     25
      155

17. 127

18.  55     125     125
19. 115     140     40
8 0
2 years ago
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What are the expressions in factored form?<br><br> 6x^2 + 4x<br><br> 4x^2 + 11x + 6<br><br> 9x^2 - 4
Alexxandr [17]
<span>6x^2 + 4x = 2x(3x + 2)

4x^2 + 11x + 6 = (4x + 3)(x + 2)

9x^2 - 4 = (3x +2)(3x - 2)</span>
7 0
2 years ago
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Suppose an aquarium has a length of 4 feet, a width of 2 feet, and is filled with water to a depth of 9 feet. A reef is placed i
BigorU [14]

Answer:

24ft^3

Step-by-step explanation:

The information that we kow about the shape of the aquarium:

length:

l=4ft

width:

w=2ft

when the reef is submerged, the water level rises 3 feet. The volume that those 3 ft represent in the aquarium will be the volume of the reef.

Thus, we calculate the volume of water "addition" with the same length and width as the aquarium but with a deep of 3 feet (thi is because the reef caused the water to rise 3 feet), and this is the volume of the reef that was added to the aquarium:

V=4ft*2ft*3ft\\V=24ft^3

The volume of the stone is 24ft^3

8 0
2 years ago
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