What is the vertex of the given quadratic function? f(x) = 3x2 + 18x – 30
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(5, 57)
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(57, 3)
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(3, 57)
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(-3, -57)
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Correct answer
Explanation
The vertex of a parabola f(x) = ax^2 + bx + c is at x = -b/(2a). Here, x = -18 / (2*3) = -3. Plugging x = -3 into the function: f(-3) = 3(-3)^2 + 18(-3) - 30 = 27 - 54 - 30 = -57. The vertex is (-3, -57).
AI explanation
The vertex x-coordinate of a quadratic function f(x) equals ax squared plus bx plus c is found using the formula x equals -b divided by 2a. Substituting a equals 3 and b equals 18 gives x equals -18 divided by 6, which is -3. Substitute x equals -3 into the function to find the y-coordinate, which is 3 multiplied by 9 plus 18 multiplied by -3 minus 30, equaling -57. Therefore, the vertex is (-3, -57).