What is y- intercept point of the graph below?
1. What is y- intercept point of the graph below?
Jawaban:
(0,-6)
Penjelasan dengan langkah-langkah:
ingat bahwa y- intercept point (titik potong sumbu y) adalah titik yang memotong sumbu y (vertikal) dan titik bertemunya garis di x=0
lokasinya pada fungsi kuadrat adalah (0,c)
misal...
x² - 2x + 3
a = 1
b = -2
c=3
maka titik potong sumbu y adalah (0, 3)
--------
di grafik, titik potong sumbu y berada di (0,-6)
2. Find the vertex in the graph of y = 3x^2 – 12x + 2. pls bantu (jgn ngasal)
Penjelasan dengan langkah-langkah:
vertex ---> sumbu simetri
y = 3x² - 12x + 2
dengan a = 3, b = -12, c = 2
maka
sumbu simetri x = -b/2a
x = -(-12)/(2)(3)
x = 12/6
x = 2
3. the graph of y = ax2 bx c has its vertex at the point (1, 5) and intersects the y-axis at (0, 1). find the values of a, b and c
Jawaban:
a = –4, b = 8, and c = 1.
Pembahasan
Fungsi Kuadrat (Quadratic Functions)Given that the vertex of y = ax² + bx + c is (1, 5), we know that the axis symmetry for this graph is x = 1, which equals to –b/(2a).
Therefore:
–b/2a = 1
⇔ b = –2a ....(i)
From that vertex, we know that y = 5 when x = 1. The value of y is the minimum or maximum value of ax² + bx + c.
Let’s substitute –2a for b, based on eq. (i).
y = ax² – 2ax + c .....(ii)
And then, substitute 5 for y and 1 for x.
5 = a(1²) – 2a(1) + c
⇔ 5 = a – 2a + c
⇔ 5 = –a + c
⇔ c = a + 5 .....(iii)
Substitute a + 5 for c in eq. (ii).
y = ax² – 2ax + a + 5 .....(iv)
The y-intercept point is at (0, 1).
Let’s plug x = 0 and y = 1 into eq. (iv).
1 = a(0²) – 2a(0) + a + 5
⇔ 1 = 0 – 0 + a + 5
⇔ 1 = a + 5
⇔ a = 1 – 5
⇔ a = –4
Plug a = –4 into eq. (i), we get:
b = –2(–4) = 8
And then, plug a = –4 into eq. (iii), we get:
c = –4 + 5 = 1
CONCLUSIONa = –4, b = 8, and c = 1.
The complete function is y = –4x² + 8x + 1.
4. 23 The graph of 2x + 4y = 15 is a straight line. Work out the gradient of the line. pls jawab
m1 = -2/4 = -1/2
straight line
m2 = -1/-1/2
m2 = 2
5. 5. The points (4, a), (5,-2) are some points on the graph of y = 2x + 7. Find without plotting the graph, (a) the value of a, (b) the value of b.
Penjelasan dengan langkah-langkah:
(4, a) ------> y = 2x + 7
a = 2 . 4 + 7
= 8 + 7
= 15
so, value of a is 15
6. Look at the graphWhat is the gradient of the line JKSelect one:a. 1/2b. 2c. -1/2d. -2
Jawaban:
gradient is equal to
[tex] \frac{y2 - y1}{x2 - x1} = \frac{7 - 3}{4 - 6} = \frac{4}{ - 2} = - 2[/tex]
7. What is the velocity/time gradient graph for the oscillator ?
Jawaban:
The gradient of speed-time and velocity-time graphs represent acceleration. The area under a speed-time graph represents the distance travelled. Likewise, the area under a velocity-time graph represents the displacement of the moving object.
Penjelasan:
Gradien grafik kecepatan-waktu dan kecepatan-waktu mewakili percepatan. Area di bawah grafik kecepatan-waktu mewakili jarak yang ditempuh. Demikian juga, area di bawah grafik kecepatan-waktu mewakili perpindahan benda yang bergerak.
8. mohon bantuannya The picture is a graph of quadratic function......
Persamaan umum fungsi kuadrat :
f(x) = Ax² + Bx + C
Diketahui grafik fungsi f(x) melewati titik :
» (3 , 0)
=> f(3) = 0
=> A.(3)² + B.(3) + C = 0
=> 9A + 3B + C = 0 ( i )
» (–1 , 0)
=> f(–1) = 0
=> A.(–1)² + B.(–1) + C = 0
=> A - B + C = 0 ( ii )
» (0 , 3)
=> f(0) = 3
=> A.(0)² + B.(0) + C = 3
=> C = 3
Subtitusikan nilai C ke ( i ) :
9A + 3B + C = 0
9A + 3B + 3 = 0
9A + 3B = –3 ( iii )
Subtitusikan nilai C ke ( ii ) :
A - B + C = 0
A - B + 3 = 0
A - B = –3 ( iv )
Eliminasi ( iii ) dan ( iv ) :
( iii ) : 9A + 3B = –3
(iv) × 3 : 3A - 3B = –9
________________ +
12A = –12 => A = –1
Subtitusikan nilai A ke ( iv ) :
A - B = –3
–1 - B = –3 => B = 2
Substitusikan nilai A, B, dan C ke persamaan fungsi kuadrat :
f(x) = Ax² + Bx + C
f(x) = (–1)x² + (2)x + (3)
Jadi, persamaan fungsi kuadrat grafik tersebut adalah : f(x)=–x²+2x+3
9. A container in the shape of a hollow cone of semi-vertical angle 30 is held with its vertex pointing downwards. Water is poured into the cone at rate of 70cm s.find the rate at which the depth of water in the cone is increasing when the depth of the water is 9 cm
Jawaban:
☺☺
Penjelasan dengan langkah-langkah:
ga ngerti? coba pake b indo
10. Refers to graph given in problems 2 above. a. If edge that connects vertex i and vertex j is named by eij, then name all edges in the graph given above. b. Write the degree of all vertices c. Represent the graph using adjacency matrices.
Jawaban:
Mengacu pada grafik yang diberikan dalam masalah 2 di atas.
a. Jika tepi yang menghubungkan simpul i dan simpul j dinamai dengan eij, maka beri nama semua sisi pada graf yang diberikan di atas.
b. Tuliskan derajat semua simpul
c. Mewakili grafik menggunakan matriks kedekatan
Penjelasan dengan langkah-langkah:
semoga membantu!
11. 1.what is the percentage of the indonesian workers who have a university degree?2.which percentage is bigger,the workers with an SMA certificate or an SMK sertificate?3.what is the educational level of the majority of indonesian workers based on the graph?
1. 4 percent workers who have a university degree
2. SMA bigger than SMK (precentage workers)
3. SD level.
12. make the graph of this equation : 2x + y = 2!
Semoga Bermanfaat
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13. Sam took tickets at the volleyball game. The graph shows the relationship between tickets sold and the amount of money collected. What is the price per ticket?
Jawaban:
Sam mengambil tiket di pertandingan bola voli. Grafik menunjukkan hubungan antara tiket yang terjual dan jumlah uang yang dikumpulkan. Berapa harga per tiketnya?
Penjelasan dengan langkah-langkah:
somoga membantu
14. the graph of x + y = -4 passes through Y-axis at the point (0, k) and passes through X-axis at the point (h, 0). what is the value of k and h?
melewati Y axis (0,k)
0 + k = -4
k = -=
melewati X axis (h,0)
h + 0 = -4
h = -4
15. Y =ax2 + bx +c Y = k For which value of k ( in term a,b and c ) will thesystem have exactly one solution? What is that solution?what is the relationship betweenthis solution you’vefound and the graph of Y = ax2 + bx + c?
its so easy...just make a substitution and use the diskriminant properties. the K is should the vertex ordinat for y=ax2+bx+c
16. the vertex of a parabola is at the origin and Q(3,-2) is a point on the parabola. Find the equation and focus of this parabola if the focus is on the negative side of the y-axis
Vertex origin = Pusat(0,0)
Melalui (3,-2)
Parabola terbuka ke kiri
[tex]y^2=4px \\ (-2)^2=4p(3) \\ 4=12p \\ p=\frac{1}{3} \\ $Persamaan umum:$ \\ y^2=-4px \\ y^2=-\frac{4}{3}x \\ $Fokus : $(0-p,0) \\ $Fokus : $(-\frac{1}{3},0)[/tex]
17. Draw the graph of y =2x-7 and find its gradient
Jawab:
Penjelasan dengan langkah-langkah:
18. The midpoint of the diagonal of a square is 2 units from the vertex of the square. Calculate area of the square.
Jawaban:
Titik tengah diagonal persegi adalah 2 satuan dari titik sudut persegi. Hitung luas persegi.
19. question A1. what is the purpose of the graph? 2. can you understand the graph easily?3. what does the graph tell us about? 4. how many quantities are shown by the graph? what are they? question B1. how many numbers of respondents spend time watching tv for 2-3 hours? 2. how many numbers of respondents spend time watching tv for 3 or more hours?3. how many hours do the 12 respondents spend watching tv?
1.answer: the graph tell who has the most respondents
20. what does the gradient of velocity/time graph for an oscillator represent
Acceleration
The gradient of speed-time and velocity-time graphs represent acceleration. The area under a speed-time graph represents the distance travelled. Likewise, the area under a velocity-time graph represents the displacement of the moving object.
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