Answers
Given:
The graphs of two parabolas.
To find:
The equation of the quadratic function with given graphs.
Solution:
(a)
The factor form of a parabola is
[tex]y=a(x-b)(x-c)[/tex]
Where, a is a constant, b and c are x-intercepts.
From the graph (a) it is clear that the graph intersect the x-axis at -1 and 3. So, b=-1 and c=3.
[tex]y=a(x-(-1))(x-3)[/tex]
[tex]y=a(x+1)(x-3)[/tex] ...(i)
Put x=0 and y=3 because the y-intercept is (0,3).
[tex]3=a(0+1)(0-3)[/tex]
[tex]3=-3a[/tex]
[tex]\dfrac{3}{-3}=a[/tex]
[tex]-1=a[/tex]
Putting a=-1 in (i), we get
[tex]y=-1(x+1)(x-3)[/tex]
[tex]y=-(x+1)(x-3)[/tex]
Therefore, the equation of the parabola is [tex]y=-(x+1)(x-3)[/tex].
(b)
The vertex form of a parabola is
[tex]y=a(x-h)^2+k[/tex]
Where, a is a constant and (h,k) is vertex.
From the the graph (b), it is clear that the vertex of the of the parabola is at point (2,0) and y-axis is (0,8). So, h=2, k=0.
[tex]y=a(x-2)^2+0[/tex]
[tex]y=a(x-2)^2[/tex] ...(ii)
Put x=0 and y=8 because the y-intercept is (0,8).
[tex]8=a(0-2)^2[/tex]
[tex]8=4a[/tex]
[tex]\dfrac{8}{4}=a[/tex]
[tex]2=a[/tex]
Putting a=2 in (ii), we get
[tex]y=2(x-2)^2[/tex]
Therefore, the equation of the parabola is [tex]y=2(x-2)^2[/tex].
Related Questions
NEED ANSWER ASAP! ON A TIMED TEST!
Four chords are drawn in the figure below, creating a quadrilateral with every vertex on the circle.
Using the special properties of this figure, determine m
Answers
Answer:
21°
Step-by-step explanation:
<DCB = 3x + 8°
< DAB = 5x + 4°
Now
<DCB + <DAB = 180° { being opposite angles of cyclic quadrilateral }
3x + 8° + 5x + 4° = 180°
8x + 12° = 180°
8x = 180° - 12°
8x = 168°
x = 168° / 8
Therefore x = 21°
Hope it will help :)
Quadratic Equations and Functions - Part 2
Graphing Quadratics Using a Table
Independent Practice
1. A model rocket was launched from a podium 5 meters above ground at a
initial velocity of 98 m/s. The function that models height (in meters) with
respect to time (in seconds) is h(t) = 5 + 98t – 4.9t2.
Part A: Complete the table below.
Time (seconds)
0
5
10
15
20
Elevation (feet)
5
Answers
Answer:
See below
Step-by-step explanation:
Given function
h(t) = 5 + 98t – 4.9t²Part AFilling in the table using the function, substitute t for each line:
time | elevation
0 | 5
5 | 372.5
10 | 495
15 | 372.5
20 | 5
Part BThe graph is attached
When the ball hits the ground, the height is 0. Substitute 0 for
h
.
h
=
−
16
t
2
−
10
t
+
200
0
=
−
16
t
2
−
10
t
+
200
−
16
t
2
−
10
t
+
200
=
0
This equation is difficult to solve by factoring or by completing the square, so solve it by applying the Quadratic Formula,
x
=
−
b
±
√
b
2
−
4
a
c
2
a
. In this case, the variable is
t
rather than
x
.
a
=
−
16
,
b
=
−
10
, and
c
=
200
.
t
=
−
(
−
10
)
±
√
(
−
10
)
2
−
4
(
−
16
)
(
200
)
2
(
−
16
)
Simplify. Be very careful with the signs.
t
=
10
±
√
100
+
12800
−
32
=
10
±
√
12900
−
32
Use a calculator to find both roots.
t
is approximately
−
3.86
or
3.24
.
Consider the roots logically. One solution,
−
3.86
, cannot be the time because it is a negative number. The other solution,
3.24
seconds, must be when the ball hits the ground.
Answer
The ball hits the ground approximately
3.24
seconds after being thrown.
pls help.........with the help of pic
Answers
Answer:
Her journey by car.
Step-by-step explanation:
3/5 is more than 3/10. I hope this helps :)
Answer: 3/10 of her journey by autorikshaw.
Step-by-step explanation:
What’s 2/10 closest to 0,1/2 or 1
Answers
Answer:
0
Step-by-step explanation:
2/10 is 2/10 away from 0, 2/10 is 3/10 away from 1/2, and 2/10 is 8/10 away from 1
Adult tickets to a basketball game cost $5. Student tickets cost $1. A total of $3,047
was collected on the sale of 1,291 tickets. How many of each type of ticket were sold?
The basketball game sold
adult tickets and
student tickets.
Answers
Answer:
The basketball game sold 439 adult tickets and 858 student tickets.
Step-by-step explanation:
A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is, in the systems of equations, one must look for the values of the unknowns, with which when replacing, they must give the solution proposed in both equations.
Adult tickets to a basketball game cost $5. Student tickets cost $1. A total of $3,047 was collected on the sale of 1,291 tickets.
With "x" the number of adult tickets sold and "y" the number of student tickets sold, you have the following system of equations:
[tex]\left \{ {{x+y=1291} \atop {5*x+1*y=3047}} \right.[/tex]
Through the substitution method, you must solve for one of the unknowns in one of the equations and substitute its value in the following one: in this case you solve for the variable y from the first equation:
y=1291 -x
and you replace in the second equation:
5*x + 1291 - x= 3047
Solving, you get:
5*x-x= 3047 - 1291
4*x= 1756
x= 1756÷4
x=439
Replacing this value in the expresion y=1291 -x you get:
y=1291 -439
y= 858
The basketball game sold 439 adult tickets and 858 student tickets.
Write down the exact value of:
a) cos 0
b) sin 30°
c) tan 0°
Answers
Answer:
cos0 = 1
sin30= 1/2
tan0 = 0
Answer:
[tex]a) cos0^o = 1\\b) sin30^o = \frac{1}{2} \\c) tan0^o =0[/tex]
Rearrange x= 3g + 2 to make g the subject
Answers
3g + 2 = x
3g = x - 2
g = (x - 2)/3
Answer:
g = 1/3 x - 2/3
Step-by-step explanation:
x =3g + 2
Switch sides:
3g + 2 = x
Take away 2 from both sides:
3g = x - 2
Divide both sides by 3:
g = 1/3 x - 2/3
If the legs of a right triangle are x, (2x - 1) and its hypotenuse is (2x + 1), what is the value of x?
Answers
Answer:
x=8
Step-by-step explanation:
(2x + 1)² = x² + (2x - 1)² = x² + (2x - 1)(2x - 1)
(2x + 1)(2x + 1) = x² + 4x²-2x-2x+1
4x²+2x+2x+1 = 5x²-4x+1
4x²+4x+1 = 5x²-4x+1
0= 5x²-4x²-4x-4x+1-1
0= x²-8x
x²-8x=0
x²=8x
x=8
all you need is in the photo please
Answers
Answer:
i don't know how to answer
Step-by-step explanation:
If 6 is multiplied by the sum of a number and 5, the result is 30. Which equation could be used to find the value of the number?
Answers
Answer:
5x6
Step-by-step explanation:
5x6
5 groups of 6
=30
In a chemistry lab, you have two vinegars. One is 8% acetic acid, and one is 9.5% acetic acid. You want to make 300mL of a vinegar with 9% acetic acid. How many milliliters of each vinegar do you need to mix together?
Answers
Answer:
4.5
Step-by-step explanation: there
QRST is a parallelogram. Find x, y, and z.
Answers
Answer:
x=5.4
y= 9
z= 11
Step-by-step explanation:
5x= 27
x= 5.4
2y-5=y+4
y=9
3z = 33
z =11
Q1. What is the ratio of 4 weeks 3 days to 6 weeks.
Q2. What is the ratio of 3 dozen eggs to 8 eggs.
Q3. How far can a bus travel in 8 litres of diesel if it can travel 144 km in 6 litres of diesel
Answer in all steps and answer quick gotta help somebody.
Answers
Answer:
Q1: 28 : 3
Q2: 36 : 3
Step-by-step explanation:
Q1 EXPLANATION:
theirs 7 days in a week and theirs four weeks
4 x 7 = 28, theirs 3 days
28 : 3
Q2 EXPLANATION:
Theirs 12 in a dozen and theirs 3 dozens
3 x 12 = 36, theirs 3 eggs
36 : 3
Q3 EXPLANATION:
8 litres is 144 km
divide both by 4
2 litres is 36 km
then times both by 3
6 litres is 108 km
yo does anyone know how to solve this
Answers
(-7, 0)
i promise im right
which best describes two figures that are similar?
Answers
Answer:
B
Step-by-step explanation:
please solve this pleaseeeee
Answers
Answer:
DIMENSIONS:
THE DOUBLE: 42.6 m cubed on both the length, width, and height
THE HALF: 10.6 m cubed on both the length width and height
THE CUBE: 21.3 m cubedon both the lengrh, width, and height
MOST HEIGHT: The Double at 42.6 m cubed
Step-by-step explanation:
We know that we have 64 m cubed. First, we should find out the volume of each cube. 64 times 2 is 128. This means the Double equals 128 in volume and half of 64 is 32. this means the Half is 32 in volume. Since these are all cubes, every side is exactly the same(or else it would be a rectangle) the formula for finding volume is length times width times height, we would divide EACH of the volumes by 3. 128 divided by 3 is 42.6 meaning the doubles dimensions would be 42.6 on each part of the cube (the lenght width and height would all be 42.6) you can check this by multiplying 42.6 by 3 which takes us back to 128. For the cube we would do 64 divided by 3 which is 21.3 pn every side and 32 divided by 3 is 10.6. The one with the most height is the double. I am not sure how to find the floor space I am super sorry but I hope this helps :)
How is the formula to find the slope between any two points the same as rise/run?
Answers
Answer:
because as long as it's the same number, the equation is still the same as long as you have the same numbers and you're using the same subtraction/addition properly
Step-by-step explanation:
Question 1 ?
Question 2 ?
Question 3 ?
Question 4 ?
Question 5 ?
Answers
Answer:
1. 90 degrees
2. 23 degrees
3. 67 degrees
4. 5 units
5. 12 units
90°
23°
67°
5 units
12 units
True and false math question
Answers
Answer:
I'm thinking it's false
Step-by-step explanation:
however, I would wait for another's opinion as well
Answer:
false
Step-by-step explanation:
just my opinion but if you think I'm wrong it's okay
How do I figure this out?
Answers
Answer:
0.75 : 1
Step-by-step explanation:
Combine like terms.
9y2 + 9(7y2-5) =
I need this for now please
Answers
Answer:
72y2-45
Step-by-step explanation:
9y2 + 9(7y2 - 5)
you multiply the 9 by the stuff in the parentheses
9y2 + 63y2 - 45
72y2-45
18 + 18 + 18 + 18 - 24 + 1 + 3 + 5 + 7 + 20 - 23 =?
Answers
Answer: 61
Step-by-step explanation:
Use addition to solve the equation.
18 + 18 + 18 + 18 - 24 + 1 + 3 + 5 + 7 + 20 - 23 = 61.
Answer:
61
Step-by-step explanation:
A biker travels 10 miles in two hours, what is his speed?
Answers
Answer:
5 mph
Step-by-step explanation:
10/2 is 5 miles in one hour.
Answer:
5mph
Step-by-step explanation:
10/2
Two students were shopping for school supplies. They need spirals which cost x dollars and pens which cost y dollars. One student bought 2 spirals and 3 pens for $8.66. Another student bought 4 spirals and 5 pens for $15.20. Find the unit cost of a spiral.
Answers
Answer:
x=1.15
y=2.12
Step-by-step explanation:
look at the picture ..........
A box of socks contains 5 white socks, 3 grey socks, 4 black socks and 1 blue sock. If Sophie
closes her eyes and randomly picks two socks from the box, what is the probability that both socks
are grey?
Answers
Answer:
1/5
Step-by-step explanation:
g(1)=0
g(n)=g(n-1)+n
g(2)=????
Answers
If g(1) = 0 and g(n) = g(n-1) + n, then g(2) = 2
The given relationship is:
g(1) = 0
g(n) = g(n-1) + n
g(2) = ?
Since g(1) is already known
g(2) = g(1) + 2
Note that g(1) = 0
Substitute g(1) = 0 into g(2) = g(1) + 2
g(2) = 0 + 2
g(2) = 2
Therefore, if g(1) = 0 and g(n) = g(n-1) + n, then g(2) = 2
Learn more on sequence here: https://brainly.com/question/6561461
Find the value of y.
Answers
Answer:
y=27
Step-by-step explanation:
3y+53=7y-55
step 1 add 55 to each side
3y+108=7y
step 2 subtract 3y from each side
108=4y
step 3 divide each side by 4
y=27
Red balloons is 15 blue balloons is 10 what is the ratio of red to blue
Answers
Answer:
3:2
Step-by-step explanation:
15 to 5 in simplest form you caan multiply by 5 so in simplest form its
5x3=15
5x2=10
so anwswer is 3:2
plz mark brinliest
.Any number that has 9 as a factor also
has 3 as a factor. Why is this
Answers
Answer:
9 is divisable by 3.
A number that has 9 as a factor can be divided by 9 so it can also be divided by 3.
If CDG ~ EDF, find the value of x.
2x+7
5x-2
48
40
Answers
Answer:
x=4
Step-by-step explanation:
48/5x-2 = 40/2x+7
48(2x+7) = 40(5x-2)
96x+336 = 200x-80
-96x -96x
336 = 104x-80
+80 +80
416/104 = 104x/104
x = 4
The value of x is equal to 4.
we have given that,
If CDG ~ EDF, find the value of x.
2x+7
5x-2
48
40
we have to determine the value of the x.
What is the similarity of the triangle?
Two triangles are similar if they have the same ratio of corresponding sides and equal pairs of corresponding angles.
48/5x-2 = 40/2x+7
48(2x+7) = 40(5x-2)
96x+336 = 200x-80
-96x -96x
336 = 104x-80
+80 +80
416/104 = 104x/104
x = 4
To learn more about a similar triangle visit:
https://brainly.com/question/2644832
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