Mathematics, 28.01.2020 10:31 jjxt126

Match the parabolas represented by the equations with their foci.
1. y=-x^2+4x+8
2. y=2x^2+16x+18
3. y=-2x^2+5x+14
4. y=-x^2+17x+7
5. y=2x^2+11x+5
6.y=-2x^2+6x+5
-pairs-
a. (-2.75, -10)
b. (2, 11.75)
c. (-4, -13.875)
d. (1.25, 17)

match numbers 1-6 with letters a-d i really need

Answers: 3

Show answers

Answers

Answer from: TravisI00

Function 1 $f(x)=- x^{2} +4x+8$

First step: Finding when f(x)

is minimum/maximum
The function has a negative value $x^{2}$ hence the f(x)

has a maximum value which happens when $x=- \frac{b}{2a}=- \frac{4}{(2)(1)}=2$ . The foci of this parabola lies on x=2

.

Second step: Find the value of y-coordinate by substituting x=2

into

which give $y=- (2)^{2} +4(2)+8=12$

Third step: Find the distance of the foci from the y-coordinate
$y=- x^{2} +4x+8$ - Multiply all term by -1 to get a positive $x^{2}$
$-y= x^{2} -4x-8$ - then manipulate the constant of y to get a multiply of 4
$4(- \frac{1}{4})y= x^{2} -4x-8$
So the distance of focus is 0.25 to the south of y-coordinates of the maximum, which is $12- \frac{1}{4}=11.75$

Hence the coordinate of the foci is (2, 11.75)

Function 2: $f(x)= 2x^{2}+16x+18$

The function has a positive $x^{2}$ so it has a minimum

First step - $x=- \frac{b}{2a}=- \frac{16}{(2)(2)}=-4$
Second step - $y=2(-4)^{2}+16(-4)+18=-14$
Third step - Manipulating f(x)

to leave $x^{2}$ with constant of 1
$y=2 x^{2} +16x+18$ - Divide all terms by 2
$\frac{1}{2}y= x^{2} +8x+9$ - Manipulate the constant of y to get a multiply of 4
$4( \frac{1}{8}y= x^{2} +8x+9$

So the distance of focus from y-coordinate is $\frac{1}{8}$ to the north of y=-14

Hence the coordinate of foci is (-4, -14+0.125) = (-4, -13.875)

Function 3: $f(x)=-2 x^{2} +5x+14$

First step: the function's maximum value happens when $x=- \frac{b}{2a}=- \frac{5}{(-2)(2)}= \frac{5}{4}=1.25$
Second step: $y=-2(1.25)^{2}+5(1.25)+14=17.125$
Third step: Manipulating f(x)

$y=-2 x^{2} +5x+14$ - Divide all terms by -2
$-2y= x^{2} -2.5x-7$ - Manipulate coefficient of y to get a multiply of 4
$4(- \frac{1}{8})y= x^{2} -2.5x-7$
So the distance of the foci from the y-coordinate is - $\frac{1}{8}$ south to y-coordinate

Hence the coordinate of foci is (1.25, 17)

Function 4: following the steps above, the maximum value is when x=8.5

and

. The distance from y-coordinate is 0.25 to the south of y-coordinate, hence the coordinate of foci is (8.5, 79.25-0.25)=(8.5,79)

Function 5: the minimum value of the function is when x=-2.75

and

. Manipulating coefficient of y, the distance of foci from y-coordinate is $\frac{1}{8}$ to the north. Hence the coordinate of the foci is (-2.75, -10.125+0.125)=(-2.75, -10)

Function 6: The maximum value happens when x=1.5

and

. The distance of the foci from the y-coordinate is $\frac{1}{8}$ to the south. Hence the coordinate of foci is (1.5, 9.5-0.125)=(1.5, 9.375)

Answer from: jayzelgaspar8441

1) (1 , -22) and (1 , 12) ⇔ (y + 5)²/15² - (x - 1)²/8² = 1

2) (-7 , 5) and (3 , 5) ⇔ (x + 2)²/3² - (y - 5)²/4² = 1

3) (-6 , -2) and (14 , -2) ⇔ (x - 4)²/8² - (y + 2)²/6² = 1

4) (-7 , -10) and (-7 , 16) ⇔ (y - 3)²/5² - (x + 7)²/12² = 1

Step-by-step explanation: I got this right on Edmentum.

Match the parabolas represented by the equations with their foci. 1. y=-x^2+4x+8 2. y=2x^2+16x+18 3.

Answer from: Quest

image result for what is another name for consecutive interior angles?

when two lines are crossed by another line (called the transversal): the pairs of angles on one side of the transversal but inside the two lines are called consecutive interior angles. in this example, these are consecutive interior angles: d and f.

step-by-step explanation:

Answer from: Quest

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x.

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x

Another question on Mathematics

Mathematics, 21.06.2019 19:20

The graph below shows the height of a projectile t seconds after it is launched. if acceleration due to gravity is -16 ft/s2, which equation models the height of the projectile correctly?

Answers: 2

Answer

Mathematics, 21.06.2019 19:30

Identify the number as a rational or irrational.explain. 127

Answers: 1

Answer

Mathematics, 21.06.2019 20:00

Someone answer asap for ! the boiling point of water at an elevation of 0 feet is 212 degrees fahrenheit (°f). for every 1,000 feet of increase in elevation, the boiling point of water decreases by about 2°f. which of the following represents this relationship if b is the boiling point of water at an elevation of e thousand feet? a. e = 2b - 212 b. b = 2e - 212 c. e = -2b + 212 d. b = -2e + 212

Answers: 1

Answer

Mathematics, 22.06.2019 00:30

What are the greatest common factor of 75 and 30

Answers: 2

Answer

You know the right answer?

Match the parabolas represented by the equations with their foci.
1. y=-x^2+4x+8
2. y=2x...

Questions