Menentukan Fungsi Kuadrat (Rumadi P20 )
- 1.
. Grafik di atas mempotong sumbu ( -2, 0 ) ( 3, 0 ) dan melalui titik ( 1, 6 ) pada grafik, maka persamaannya adalah :
- A.
A . y = x2 + x + 6
- B.
B . y = x2 + 2x + 6
- C.
C. y = -x2 + 2x - 6
- D.
D y = -x2 + x + 6
- E.
E y = 2x2 + x + 6
Correct Answer
D. D y = -x2 + x + 6Explanation
The graph intersects the x-axis at (-2, 0) and (3, 0), which means that the equation has roots at x = -2 and x = 3. The graph also passes through the point (1, 6), which means that when x = 1, y = 6. The equation that satisfies these conditions is y = -x^2 + x + 6.Rate this question:
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- 2.
. f (x) = x2 – 7x + 15, jika f (a) = 5, maka nilai a yang memenuhi adalah
- A.
A. 2 atau 5
- B.
B. – 2 atau 5
- C.
C. – 2 atau – 5
- D.
D. 4 atau 5
- E.
E. – 4 atau – 5
Correct Answer
A. A. 2 atau 5Explanation
To find the values of a that satisfy the equation f(a) = 5, we can substitute 5 for f(a) in the given equation f(x) = x^2 - 7x + 15. This gives us the equation 5 = a^2 - 7a + 15. Rearranging the equation, we get a^2 - 7a + 10 = 0. Factoring this quadratic equation, we have (a-2)(a-5) = 0. Therefore, the values of a that satisfy the equation f(a) = 5 are a = 2 or a = 5.Rate this question:
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- 3.
Tentukan persamaan grafik yang mempunyai titik balik di titik ( 1, -1 ) serta melalui ( 2, 3 ) !!!
- A.
A. y = x2 - 8x + 3
- B.
B. y = 2x2 - 8x + 3
- C.
C. y = 3x2 - 8x + 3
- D.
D.y = 4x2 - 8x + 3
- E.
E. y = 5x2 - 8x + 3
Correct Answer
D. D.y = 4x2 - 8x + 3Explanation
The equation of the graph with a turning point at (1, -1) and passing through (2, 3) can be found by substituting the coordinates into the equation and solving for the unknowns. In this case, substituting (1, -1) into the equation will give us -1 = 4 - 8 + 3, which is true. Substituting (2, 3) into the equation will give us 3 = 16 - 16 + 3, which is also true. Therefore, the equation that satisfies both conditions is y = 4x^2 - 8x + 3.Rate this question:
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- 4.
Grafik fungsi yang melalui tiga buah titik yaitu (-1, 3), (1, -3), dan (4, 0), maka fungsi persamaannya adalah :
- A.
A. y = 4/5x2 - 3x - 4/5
- B.
B. y = 3/5x2 - 3x - 4/5
- C.
C. y = 2/5x2 - 3x - 4/5
- D.
D. y = 1/5x2 - 3x - 4/5
- E.
E. y = 5x2 - 3x - 4/5
Correct Answer
A. A. y = 4/5x2 - 3x - 4/5Explanation
The given points (-1, 3), (1, -3), and (4, 0) can be used to determine the coefficients of the quadratic equation. By substituting the x and y values of each point into the equation, we can form a system of equations. Solving this system will give us the values of the coefficients. The resulting equation is y = 4/5x^2 - 3x - 4/5, which matches option A.Rate this question:
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- 5.
Tentukan persamaan grafik fungsi kuadrat yang melalui titik (–1 , 0) , ( 1 , 8 ) dan ( 2, 6 ).
- A.
A. y = –x2 + 4x + 6
- B.
B. y = –2x2 + 4x + 6
- C.
C. y = –3x2 + 4x + 6
- D.
D. y = –2x2 + 3x + 6
- E.
E. y = –2x2 + 4x + 5
Correct Answer
B. B. y = –2x2 + 4x + 6Explanation
The equation of a quadratic function can be determined by substituting the given points into the general form of the equation, which is y = ax^2 + bx + c. By substituting the coordinates (-1, 0), (1, 8), and (2, 6) into the equation, we can solve for the values of a, b, and c. After substituting the values, we find that the equation y = -2x^2 + 4x + 6 satisfies all three points. Therefore, the correct answer is B. y = -2x^2 + 4x + 6.Rate this question:
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- 6.
Tentukan fungsi kuadrat yang grafiknya memotong sumbu-X di titik (–5,0) dan (1,0), serta melalui titik (–3, –8) !
- A.
A.y = x2 + x – 5
- B.
B.y = x2 - x – 5
- C.
C.y = x2 + 4x – 5
- D.
D y = x2 - 4x – 5
- E.
E.y = x2 + 4x + 5
Correct Answer
C. C.y = x2 + 4x – 5Explanation
The correct answer is C.y = x2 + 4x - 5. This is because the given quadratic function intersects the x-axis at the points (-5,0) and (1,0), which means that the roots of the equation are -5 and 1. Therefore, the equation can be written in the form y = (x - (-5))(x - 1), which simplifies to y = (x + 5)(x - 1). Expanding this equation gives y = x2 + 4x - 5, which matches the given answer.Rate this question:
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- 7.
Tentukan fungsi kuadrat yang grafiknya mempunyai titik tertinggi / titik puncak / titik ekstrim (1,3) dan melalui titik (0,0).
- A.
A.y = –3x2 + 6x
- B.
B. y = 3x2 + 6x
- C.
C. y = –3x2 - 6x
- D.
C. y = 3x2 - 6x
- E.
E. y = x2 + 6x
Correct Answer
A. A.y = –3x2 + 6xExplanation
The correct answer is A because it is the only equation that satisfies the given conditions. The equation represents a quadratic function with a negative coefficient for the x^2 term, indicating a downward-opening parabola. The coefficient of the x term is positive, indicating that the parabola opens to the left. The vertex of the parabola is at (1,3), which means that the highest point of the graph is at this coordinate. Additionally, the equation passes through the point (0,0), confirming that it is the correct quadratic function.Rate this question:
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- 8.
Tentukan fungsi kuadrat grafiknya mel. 3 buah titik (-1,0), (2,-9) dan (4,-5)
- A.
A. y = x2 - 2x - 5
- B.
B. y = x2 - 4x - 5
- C.
C. y = x2 - 4x + 5
- D.
D. y = x2 - 6x - 5
- E.
E. y = x2 - 6x + 5
Correct Answer
B. B. y = x2 - 4x - 5Explanation
The given points (-1,0), (2,-9), and (4,-5) can be used to determine the coefficients of the quadratic function. By substituting these points into the general form of a quadratic function, y = ax^2 + bx + c, we can solve for a, b, and c. After substituting the values, we find that a = 1, b = -4, and c = -5. Therefore, the quadratic function that represents the graph is y = x^2 - 4x - 5, which matches option B.Rate this question:
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Mar 21, 2023Quiz Edited by
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Oct 15, 2018Quiz Created by
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