What is the equation of axis of symmetry of the given quadratic equation? * y = x2 – 8x - 9
1. What is the equation of axis of symmetry of the given quadratic equation? * y = x2 – 8x - 9
Jawaban:
x = 4
Penjelasan dengan langkah-langkah:
x = -b/2a
= -(-8)/2(1)
= 4
Jawaban:
x = 4
Penjelasan dengan langkah-langkah:
semoga membantu:)
2. If X1 and x2 is quadratic equation roots x2 - x+2 = 0. the newquadratic equation that has roots 2x1-2 and 2x2 - 2 is .....
Penjelasan dengan langkah-langkah:
Itu ya de jawabannya. Mohon maaf kalau kurang jelas
3. Let a and b is the roots of quadratic equation -2x-3x+2=0. The value of ab+ab is
-5x.2+-5x.2 ,this is of ab+ab i hope this answer could help you
4. 2. Given a quadratic equation 2(x-5)²= 4(x + 7).(a) express the equation in general form, that is ax²+bx+c=0
2(x - 5)² = 4(x + 7)
2(x² - 10x + 25) = 4x + 28
2x² - 20x + 50 = 4x + 28
2x² - 20x + 50 - 4x - 28 = 0
2x² - 24x + 22 = 0
x² - 12x + 11 = 0
Jawab:
2(x-5)² = 4(x+7)
2(x²-10x+25) - 4(x+7)=0
2x²-20x+50-4x-28=0
2x²-24x+22=0
so in general from is
2x²-24x+22=0
5. if x = 2 is a root of a quadratic equation [tex]a {x}^{2} + 2ax - 3 = 0[/tex]then the value of a is ....A. integer B. rationalC. negativeD. irrationaluse the methods and steps !!
Jawaban:
B. rational
Penjelasan dengan langkah-langkah:
ax² + 2ax - 3 = 0
Because x = 2 is a root, substitution x = 2 to ax² + 2ax - 3 = 0 to find the value of a
a × 2² + 2a × 2 - 3 = 0
4a + 4a - 3 = 0
8a - 3 = 0
8a = 3
a = 3/8
the value of a is 3/8
3/8 is rationalnumberbecause the number can be expessed in form a/b and have definite results (can change into decimal number, percent, etc)
6. Given the quadratic equation [tex]\tt{} {x}^{2} - 5x + 6 = 0 [/tex] find the value of: A. [tex]\tt{} x _{1} + x_2[/tex] B. [tex] \tt{}x_1.x_2[/tex] C. [tex] \tt{}x_ {1 }^{2} + x_ {2}^{2} [/tex] D. Determine the type of root of the quadratic equation and its discriminant
Penjelasan dengan langkah-langkah:
[tex]{x}^{2} - 5x + 6 = 0 \\ (x - 3)(x - 2) = 0 \\ x - 3 = 0 \: \: \: \: x - 2 = 0\\ x = 3 \: \: \: \: \: \: \: x = 2[/tex]
a. misalkan x1 = 3 dan x2 = 2 maka
x1 + x2
= 3 + 2
= 5
b. x1 • x2
= 3• 2
= 6
c. x1^2 + x2 ^2
= 3^2 + 2^2
= 13
d. D = b^2 - 4ac (a =1, b= 5, c =6)
= 5^2 - 4 • 1 • 6
= 10 - 24
= -14 ( karena D < 0, fungsinya maka persamaan kuadrat tersebut mempunyai akar imajiner / tidak nyata / tidak real)
semoga membantu. maaf jika salah
7. 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
8. One solution of the quadratic equation x^2 + px + 12=0 is 3, then p=... and another solution is...
x² + px + 12 = 0
salah astu penyelesaian x = 3
maka
x² + px + 12 = 0
⇒ (3)² + p(3) + 12 = 0
⇒ 9 + 3p + 12 = 0
⇒ 3p = -21
⇒ p = -7
Sehingga
x² - 7x + 12 = 0
⇒ (x - 3)(x - 4) = 0
maka
x - 3 = 0 ⇒ x = 3
x - 4 = 0 ⇒ x = 4
Jadi, p = -7, dan penyelesaian yang satunya = 4
Terimakasih semoga membantu
9. solve the quadratic equation below
Step by step explanation
_________
Nomor 1
_________
[tex]\begin{aligned}\rm \frac{5x+12}{3x}&=\rm x\\\rm 5x+12&=\rm 3x^2\\0&=\rm 3x^2-5x-12\\0&=\rm (3x+4)(x-3)\\&\bf x=-\frac{4}{3}~atau~x=3\end{aligned}[/tex]
_________
Nomor 2
_________
[tex]\begin{aligned}\rm \frac{20-8k}{k-5}&=\rm 3k\\\rm 20-8k&=\rm 3k^2-15k\\0&=\rm 3k^2-15k+8k-20\\0&=\rm 3k^2-7k-20\\0&=\rm (3k+5)(k-4)\\&\bf k=-\frac{5}{3}~atau~k=4\end{aligned}[/tex]
10. Given one of the roots of the quadratic equation px2- 4x + 3p -8 =0 is 1 . Calculate the value of p
Jawab:
p = 3
Penjelasan dengan langkah-langkah:
salah satu akar = 1
persamaan nya= p[tex]x^{2}[/tex]-4x+3p-8 = 0
masukkan angka 1 ke persamaan:
p[tex](1^{2})[/tex] -4(1) +3p -8 = 0
p-4+3p-8 = 0
4p = 12
p=3
11. write a quadratic equation for the area of the floor in terms of w
What are the measurements?
12. Given one of the roots of the quadratic equation x 2 + kx – 3 = 0 is 3. Find the value of k.
Jawaban:
x²+kx-3=0
3²+3k-3=0
9+3k-3=0
3k+6=0
3k=-6
k=-2
barangkali ada yg ditanyalan dm dan follow ig @alwi_dj
13. 1) What is the y-intercept of the quadratic equation below? * y = x2 - 6x + 9
Penjelasan dengan langkah-langkah:
titik potong persamaan kuadrat
y = x² - 6x + 9
- titik potong terhadap sumbu y, x = 0
y = 0² + 6(0) + 9
y = 9
titik potongnya (0, 9)
- titik potong terhadap sumbu x, y = 0
x² - 6x + 9 = 0
(x - 3)(x - 3) = 0
x = 3
titik potongnya (3, 0)
14. Write the quadratic equation given its solution x = 3, x = 4
x=3 and x=4
We get
x-3 = 0 and x -4 = 0
Next to do
(x-3)(x-4) = 0
x²-7x+12 = 0
Hope this will help
15. Given quadratic equation y = -×2-x+20a. Find what is the zero value
Using the quadratic formula
[tex] \frac{ - b \: ± \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
[tex]x = \frac{ - ( - 1)± \sqrt{( - 1 {)}^{2} - 4( - 1)(20)} }{2( - 1)} = [/tex]
[tex] x = \frac{1± \sqrt{81} }{ - 2} = [/tex]
[tex]x1= \frac{1 + 9}{ - 2} = - 5[/tex]
[tex]x2 = \frac{1 - 9}{ - 2} = 4[/tex]
ANSWER:
X1=(-5)
X2=4
16. The quadratic equation ( 1 + k) xkuadrat 4kx + 9 = 0 has two distinct real number roots. The range of values of k is....
syarat memuliki 2 akar real yang berbeda adalah D > 0
D = b² - 4ac
(1 +k)x² + 4kx + 9
D > 0
(4k)² - 4(1+k)(9) > 0
16k² - 36 - 36 k > 0
4k² - 9k - 9 > 0
(4k + 3)(k - 3) > 0
k = -3/4 ATAU k = 3
_+__|__-__|__+__
-3/4 3
karena kurang dari, maka daerah yang negatif jawabannya -3/4 < x < 3
Maaf kalau salah^^
17. The roots of the quadratic equation 3x²-17+45=25x-54 are......
• 3x² -17x + 45 = 25x - 54
• 3x² - 17x + 45 - 25x + 54 = 0
• 3x² - 17x - 25x + 45 + 54 = 0
• 3x² - 42x + 99 = 0
------------------------- : 3
• x² - 14x + 33 = 0
• (x-3)(x-11) = 0
~ x¹ → x-3 = 0
~ x¹ → x = 3
~ x¹ = 3
~ x² → x-11 = 0
~ x² → x = 11
~ x² = 11
The roots :
x1 = 3 & x2 = 11
→ x = { 3 , 11 }3x² - 17 + 45 = 25x - 54
3x² + 28 = 25x - 54
3x² - 25x + 82 = 0
Solve it by quadratic formula!
a = 3, b = -25, c = 82
x₁₂ = [-b +- √(b² - 4ac)] / (2a)
= {-(-25) +- √[(-25)² - 4.3.82]} / (2.3)
= (25 +- i√359) / 6
x₁ = 25/6 + (i√359) / 6 or
x₂ = 25/6 - (i√359) / 6
18. given that 2 is the only root of the quadratic equation px2 + qx - 8 =0, fibd the value of p and q
PERSAMAAN KUADRAT
X SMA
It means
x1 + x2 = 4
-q / p = 4
-q = 4p
and
x1x2 = 4
-8/p = 4
p = -2
Hence,
q = -4p
q = 8
19. Quiz for Math ( Part 2 ) (2.1)Quadratic Formula Question. If X1 and X2 is roots equation quadratic of x² + x - m = 0, and m is postive constant. Determine value of X1/X2 + X2/X1
Diketahui x₁ dan x₂ adalah akar-akar persamaan : x² + x - m = 0
Maka berlaku :
[tex]x_1 \: + \: x_2 \: = \: -\frac{1}{1}[/tex]
[tex]x_1 \: + \: x_2 \: = \: -1[/tex]
[tex]x_1.x_2 \: = \: -\frac{m}{1}[/tex]
[tex]x_1.x_2 \: = \: -m[/tex]
[tex]\frac{x_1}{x_2} \: + \: \frac{x_2}{x_1} = \frac{{x_1}^2 \: + \: {x_2}^2}{x_1.x_2}[/tex]
[tex]\frac{x_1}{x_2} \: + \: \frac{x_2}{x_1} = \frac{(x_1 \: + \: x_2)^2 \: - \: 2.x_1.x_2}{x_1.x_2}[/tex]
Substitusikan nilai (x₁ + x₂) dan nilai (x₁.x₂).:
[tex]\frac{x_1}{x_2} \: + \: \frac{x_2}{x_1} = \frac{(-1)^2 \: - \: 2.(-m)}{-m}[/tex]
[tex] \boxed{ \boxed{\frac{x_1}{x_2} \: + \: \frac{x_2}{x_1} \: = \: -\frac{1 \: + \: 2m}{m}}}[/tex]
Karena diketahui m bernilai positif, maka hasil perhitungan tidak berubah.
20. Equation of a quadratic functionf(x)=x+8 will cut the X-axis at the point (memotong sumbu X pada) …
Uraian lihat foto yahMapel Matematika
Bab Persamaan Garis
f akan memotong sb.x apabila y = 0
f(x) = x + 8
0 = x + 8
-8 = x
Jadi f(x) = x + 8 akan memotong sumbu x pada x = -8
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