The safety inspector notes that Ray also needs to plan for a vertical ladder through the center of the coaster's parabolic shape for access to the coaster to perform safety repairs. Find the vertex and the equation for the axis of symmetry of the parabola, showing your work, so Ray can include it in his coaster plan.

f (x) = 3x^2+9x+12

Question

Mathematics

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12 July, 15:19

The safety inspector notes that Ray also needs to plan for a vertical ladder through the center of the coaster's parabolic shape for access to the coaster to perform safety repairs. Find the vertex and the equation for the axis of symmetry of the parabola, showing your work, so Ray can include it in his coaster plan.

f (x) = 3x^2+9x+12

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Answers (1)

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Hamza Ruiz · Answer 1

You can rearrange f (x) as:

f (x) = 3 (x^2 + 3x) + 12 = 3 (x+1.5) ^2 + 5.25

So you can see the vertex is at (0,5.25) when x = - 1.5

The axis of symmetry then lies in x = - 1.5