1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Solnce55 [7]
2 years ago
14

Match the parabolas represented by the equations with their foci.

Mathematics
1 answer:
Elenna [48]2 years ago
8 0

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 f(x) 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 y=79.25. 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 y=-10.125. 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 y=9.5. 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)

You might be interested in
What is 30 miles in 5 hours the rate and the unit rate because I need help
just olya [345]
The answer should be 15 miles per hour.
6 0
3 years ago
5 ft 9 ft<br> gft/ 7H-<br> 2 ft<br> 13 ft<br> Surface Area:<br> Volume:
Jet001 [13]

Answer:           you like it if I could double the height of your cat food can?” 6 in. 7 in. 15 cm. 30 cm. 13 ft. 6 ft ... 3 ft. 2 ft. 4 ft. 2. 5 m. 8 m. 8 m. Areas of bases. Areas of lateral faces. Exercises 7–9. Lesson Tutorials ... WRAPPING PAPER A cube-shaped gift is.

8 0
3 years ago
Solve for the value of x ​
Marrrta [24]

Answer:

38

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Adi used algebra tiles to represent the product (negative 2 x minus 1)(2 x minus 1). An algebra tile configuration. 4 tiles are
Hunter-Best [27]

Answer:

Step-by-step explanation:

c

8 0
3 years ago
Read 2 more answers
Please help!<br> 40 POINTS for you PLUS A THANKS (both on answer and profile), 5 STAR and BRAINLIEST
stepladder [879]
Sorry for bad hand writing

3 0
2 years ago
Other questions:
  • Last one lol I promise
    7·1 answer
  • A square has a perimeter of 28 yd. what is the length of each side
    7·1 answer
  • Solve: 1/4 of x is 6 =
    14·2 answers
  • Find the range of the function for the given domain.
    7·2 answers
  • Use the graph to write a linear function that relates y to x.
    12·2 answers
  • Identify different geometrical shapes associated with Rashtrapati Bhavan.
    5·1 answer
  • Please answer will give branliest eeeeeee
    7·1 answer
  • Write an equivalent expression for the area 2(3x+4)
    13·1 answer
  • What is the area of parallelogram ABCD?
    5·2 answers
  • Select the expressions that are equivalent to (4p + 6) + (−5p + 3)
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!