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What is the maximum or minimum point for the curve y = -3x2 − 12x + 5 ?
- a)A minimum at (-2, 17)
- b)A maximum at (-2, 17)
- c)A minimum at (2, -31)
- d)A maximum at (2, -31)
Correct answer is option 'B'. Can you explain this answer?
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What is the maximum or minimum point for the curve y = -3x2 − 12...
First find the first and second derivatives:
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What is the maximum or minimum point for the curve y = -3x2 − 12...
Identifying the Curve
The given equation is in the form of a quadratic function: y = -3x^2 - 12x + 5. This is a downward-facing parabola due to the negative coefficient of the x^2 term.
Finding the Vertex
To find the vertex of the parabola, we can use the formula x = -b / 2a, where a = -3 and b = -12. Substituting these values, we get x = -(-12) / 2(-3) = 2. This means the x-coordinate of the vertex is 2.
Substitute x into the Equation
Next, substitute the x-coordinate back into the original equation to find the y-coordinate. y = -3(2)^2 - 12(2) + 5 = -3(4) - 24 + 5 = -12 - 24 + 5 = -31.
Conclusion
The vertex of the parabola is at (2, -31), which means the curve has a maximum point at (2, -31). Therefore, the correct answer is option B.
The given equation is in the form of a quadratic function: y = -3x^2 - 12x + 5. This is a downward-facing parabola due to the negative coefficient of the x^2 term.
Finding the Vertex
To find the vertex of the parabola, we can use the formula x = -b / 2a, where a = -3 and b = -12. Substituting these values, we get x = -(-12) / 2(-3) = 2. This means the x-coordinate of the vertex is 2.
Substitute x into the Equation
Next, substitute the x-coordinate back into the original equation to find the y-coordinate. y = -3(2)^2 - 12(2) + 5 = -3(4) - 24 + 5 = -12 - 24 + 5 = -31.
Conclusion
The vertex of the parabola is at (2, -31), which means the curve has a maximum point at (2, -31). Therefore, the correct answer is option B.
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What is the maximum or minimum point for the curve y = -3x2 − 12x + 5 ?a)A minimum at (-2, 17)b)A maximum at (-2, 17)c)A minimum at (2, -31)d)A maximum at (2, -31)Correct answer is option 'B'. Can you explain this answer?
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