Write the equation of the following parabolae in their canonical form and hence find their vertices, foci and directrix.
1.
[tex] {y}^{2} - 6y - 2x + 19 = 0[/tex]
2.
[tex] {x}^{2} + 4x + 4y + 16 = 0[/tex]
Answers
Given:
y² - 6y - 2x + 19 = 0This is a horizontal parabola.
Canonical form of horizontal parabola is:
4a(x - h) = (y - k)², where (h, k) is vertexFocus is:
F(h + a, k)Directrix is:
x = h - aConvert the equation:
y² - 6y - 2x + 19 = 0y² - 6y + 9 - 2x + 10 = 0(y - 3)² = 2x - 10(y - 3)² = 4(1/2)(x - 5)We got:
h = 5, k = 3, a = 1/2Focus is:
F(5 + 1/2, 3) = F(5.5, 3)Directrix is:
x = 5 - 1/2 = 4.5#2Given:
x² +4x + 4y + 16 = 0This is a vertical parabola.
Canonical form of vertical parabola is:
4a(y - k) = (x - h)², where (h, k) is vertexFocus is:
(h, k + a)Directrix is:
y = k - aConvert the equation:
x² + 4x + 4y + 16 = 0x² +4x + 4 + 4y + 12 = 0(x + 2)² = -4y - 12(x + 2)² = 4(-1) (y + 3)We got:
h = - 2, k = -3, a = - 1Focus is:
F(-2, -3 - 1) = F(-2, - 4)Directrix is:
y = -3 - (-1) = - 2
Related Questions
helpppppppppppppppppppppppppppp
Answers
Answer:a is 14, b is 70%, c is 250
Step-by-step explanation:
Jim wants to collect at least 25 coins for his coin collection. He has already collected 5 coins. The inequality shown can be used to fin n, the number of coins Jim still needs to collect.
n + 5 _> 25
Which inequality represents the solution set for this situation?
A. n _> 20
B. n _< 20
C. n _< 30
D. n _> 30
Answers
Answer:
Step-by-step explanation:
n _> 25 - 5
n _> 20
Answer:
n ≥ 20
Step-by-step explanation:
n + 5 ≥ 25
n + 5 − 5 ≥ 25 − 5
n ≥ 20
The Coney Island Boardwalk is 2.7 miles long.
A person walks at the average speed of 3 mph.
How long will it take the person to walk the boardwalk to the end and back?
Answers
Answer = 1.8
Step 1) 3 ÷ 2.7 = 0.900
Step 2) 0.900 x 2 = 1.8
Time taken by the person to walk the boardwalk to the end and back is 0.9 hours.
Given that, The Coney Island Boardwalk is 2.7 miles long.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
A person walks at the average speed of 3 mph.
We know that, speed = Distance/Time
= 2.7/3
= 0.9 hours
Hence, time taken by the person to walk the boardwalk to the end and back is 0.9 hours.
To learn more about the speed, distance, and time visit:
brainly.com/question/4978052.
#SPJ2
in triangle abc it is given that AB =9 cm Bc=6cm and Ca = 7.5 cm also
triangle def is given that ef =8 cm and triangle def similar to triangle abc then perimeter of triangle def is
Answers
Answer:
Make me as brain liest plz
The perimeter of triangle DEF is; 30 cm
Similar TrianglesWe are given dimensions of Triangle ABC as;
AB = 9 cmBC = 6 cmCA = 7.5 cmThus;
Perimeter of Triangle ABC = 9 + 6 + 7.5 = 22.5 cm
We are told that Triangle DEF is similar to Triangle ABC.
This means that the ratio of corresponding sides must be equal to the ratio of their perimeter.
Side EF corresponds to side BC. Thus;
Perimeter of Triangle DEF/22.5 = 8/6
Cross multiply to get;
Perimeter of Triangle DEF = (22.5 × 8)/6
Perimeter of Triangle DEF = 30 cm
Read more on similar triangles at; https://brainly.com/question/14285697
How many solutions can be found for the system of linear equations represented on the graph?
A) no solution
B) one solution
C) two solutions
D) infinitely many solutions
Answers
Answer:
A) No solution
Step-by-step explanation:
Given the systems of linear equations, y = 2x + 1 and y = 2x - 1:
Both equations in the system have the same slope, m = 2, thus forming parallel lines. Since their lines are parallel from each other, then it means that their lines will never intersect.
Therefore, the given systems of linear equation is an inconsistent system that has no solution.
help me with #29 please
Answers
Answer:
which one is 29???
Step-by-step explanation:
Please help me I will give best answer brainliest
Answers
Answer:
i would help but i can't understand that im sry
Step-by-step explanation:
3. /9.49 thanks
Answer:
4. search it you can find it
What is the the correct equation to find the value of X?
Answers
Answer:
The first blue option or 8x - 17 = 5x + 19
Step-by-step explanation:
They are vertical angles, so they will be set equal to each other.
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
A two digit number is four times the sum and three times the product of its digit. Find the number.
Answers
Z=3 evaluar -[z-(-z)+z]Por favor alguien que me ayude
Answers
Please solve.
Picture below
Answers
Answer:
1) -2x-11
2) 1.3x-3
3) 5k-20
4) 21.84
Step-by-step explanation:
-2x-7+(-4) -2x-7-4 -2x-11
5.2x+9-12-3.9x 1.3x+9-12 1.3x-3
5(k-4) distribute 5k-20
5.46÷0.25=21.84
help me please !!!!
Answers
Answer:
graph X only
Step-by-step explanation:
because with the rate of change it makes a straight line
A car traveled 35 miles per hour. In how many hours did it travel 280 miles?
Answers
Answer:
8
Step-by-step explanation:
280/35=8
Answer:
8 hours.
Step-by-step explanation:
280/35 = 8
Please help. ASAP. Work out, giving your answer in its simplest form:
3 1/2 divided by 2 3/5
Answers
Answer:
26/35
Step-by-step explanation:
1. First to divide the 3 1/2 by 2 3/5 you have to turn them both into improper fractions
First take 3 1/2. You have to multiply the whole number (3) by the denominator (2) and you would get 6. Then you would add then you add the product (6) to the numerator (1) and get 7.
You keep the denominator the same so the improper fraction is 7/2
Do the same thing to 2 3/5 and the improper fraction is 13/5
2. Now we can divide 13/5 by 7/2 using "keep, change, flip"
Keep: 13/5
Change: division to multiplcation
Flip: 7/2 to make 2/7
Your new equation is 13/5 × 2/7. Multiplcation is easy so you just have to multiply staight across: 13 × 2 and 5 × 7 giving you 26/35
If you divide 35 by 26 you will get 1.34 and a bunch of other numbers but I usually stop at two decimal places
hope this helps :)
If f(x) = 2x^2-4 find f(-1)
Answers
f(-1) = 2·(-1)^2-4
= 2 (1) - 4
= 2 - 4
= -2
Determine the rate of change between the points (-1,-1) and (1,-1).
Answers
Answer:
[tex]\displaystyle m = 0[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinate Planes
Coordinates (x, y)Slope Formula: [tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]Step-by-step explanation:
*Note:
Rate of change is slope.
Step 1: Define
Identify.
Point (-1, -1)
Point (1, -1)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m.
Substitute in points [Slope Formula]: [tex]\displaystyle m = \frac{-1 + 1}{1 + 1}[/tex][Order of Operations] Simplify: [tex]\displaystyle m = \frac{0}{2}[/tex]Simplify: [tex]\displaystyle m = 0[/tex]pls help me and pls no link dont try me
Answers
Answer:
red line
the red line has a slope of -1 by looking at the coordinates,
it also intersects the given point (1,-1)
CAN SOMEONE PLEASE HELP ASAP I WILL GIVE 30 POINTS AND MARKED AS BRAINLIEST
Answers
Answer:
it's the middle one
Step-by-step explanation:
Slope escape room I need help ✋
Answers
Answer:
feid
Step-by-step explanation:
1. slope = -5/1
2. slope = 9
3. slope = -1/3
4. slope = 3/1
Will mark brainliest...no guessing please :)
Answers
Answer:
A
Step-by-step explanation:
We can calculate the equation of the lines based on two points. First line m:
y = ax +b
where a is the slope and b is the y-intercept. To find the slope we use the x and y of the points as:
a = [tex]a = \frac{y_1-y_2}{x_1-x_2} = \frac{4- -32}{2- -4} = \frac{36}{6} = 6.[/tex]
So:
y = 6x + b
we can find the y intercept by substituting the x and y for one of the points:
solving for b:
b=-32-(6)(-4)= -8.
So the equation is:
y = 6x - 8.
We can change it to:
y + 8 = 6x
8 = 6x - y.
So it’s (A).
Hope that helps!
Answer:
B I think
Step-by-step explanation:
I will give BRAINLIEST. Could someone give an answer along with a brief explanation pls.
Answers
Answer:
y=[tex]\frac{3}{4}[/tex]x-2
Step-by-step explanation:
Since it will be parallel that means m=[tex]\frac{3}{4}[/tex]
then you can use point slope form (y-y1)=m(x-x1): y+5=[tex]\frac{3}{4}[/tex](x+4)
then you can distribute the [tex]\frac{3}{4}[/tex]: y+5=[tex]\frac{3}{4}[/tex]x+3
then subtract 5: y=[tex]\frac{3}{4}[/tex]x-2
Nikko runs 6 miles a day and 3 days a week. How many weeks will it take Nikko to run 198 miles?
Answers
Answer:
11 weeks
Step-by-step explanation:
6*3 = 18
He runs 18 miles per week
To find out many weeks it will take Nikko to run 198 miles we do
198/18 = 11 weeks
Answer:
11 weeks
Step-by-step explanation:
6 x 3 = 18
198 divided by 18 is eleven
have a great day!
Can someone tell me the answer
Answers
Answer:
31 1/4
Step-by-step explanation:
Select the number that would make this statement true: 344 ÷ ________ = 34.4
Question 2 options:
104
103
102
101
Answers
Answer:
103
Step-by-step explanation:
I think
find the value of a b and c.
Answers
Answer:
a= 90
2a= 135
b=45
c= 45
I think x
Step-by-step explanation:
Last year, a gardening store ordered 530,570 potted plants. This year, they ordered 424,456 potted plants. What is the percent of decrease in the number of potted plants ordered annually?
Answers
Answer:
last year = 530570
this year = 424456
decreased plants = 530570-424456 = 106114
decreased percent = 106114÷530570×100%
= 20%
therefore 20% is the decrease precent in the number of potted plants ordered anually
Please Help!! Asap!!
A local club team is holding tryouts for six spots on the soccer team. Since there is not much time before a very important tournament they need to select the best players. Which method would be the best to ensure they select the "most talented" soccer players?
A. They watch the players during tryouts and then put them on a list in order from the most skilled to the least skilled and then select the top six from the list.
B. The first day of tryouts they select the first six that show up as they figure those are the most eager for a spot.
C. They place all of the names of the people trying out in a hat and then select six out of the hat. Those are the ones that are chosen.
D. They watch the players during tryouts and then put them on a list in order from the most skilled to the least skilled and then select the top three and the bottom three from the list.
Answers
Answer:
A because it's most likely to be like that at tryouts
2. French Vanitta K-Cups that originally
cost $5.99 are now on sale for $4.75.
Answers
Answer:
20.7% is the % decrease.
Step-by-step explanation:
If you are finding the % of decrease then see below.
% Decrease = (Original Cost - New Cost ) ÷ Original Cost × 100
5.99 - 4.75 = 1.24
1.24 ÷ 5.99 = .2070
.2070 × 100 = 20.7%
Plsss help It due tmr plsss
Answers
Answer: 50
Step-by-step explanation:
exterior angles are supplement of interior angle therefore the 110 thing must be 70, also youre given 60 so 70+60=130
50 is missing from 180
A board that is
16
feet long is cut into three pieces. If the length of the first piece is
3
5
6
feet and the length of the second piece is
4
5
6
feet, how long is the remaining piece of board?
