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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.

My parabola is f(x)=2x^2+8x+6.

Hi everyone! I've been working on an assignment literally all day and I only have to more questions to go! Can someone please help me with this one?
Please get back to me as soon as possible!

Respuesta :

jcherry99
Remark
You need to complete the square.

Solution
y = 2x^2 + 8x + 6  Put brackets around the first 2 terms.
y = (2x^2 + 8x) + 6 Take out the common factor of 2
y = 2(x^2 + 4x) + 6  Take 1/2 the coefficient of the linear term (4x) and square it.
y = 2(x^2 + 4x + (4/2)^2 ) + 6  The 6 is not affected yet.
y = 2(x^2 + 4x + 2^2) + 6
y = 2(x^2 + 4x + 4) + 6          Take twice the third term and subtract it from 6
y = 2(x^2 + 4x + 4) + 6 - 2*4
y = 2(x^2 + 4x + 4) + 6 - 8
y = 2(x^2 + 4x + 4) - 2            Express the 3 terms inside the brackets as a square.

y = 2(x + 2)^2 - 2

The vertex is at (-2,-2) and the axis of symmetry is x = - 2

I'll post this much and edit it to include a graph, which you should always make for a problem like this one.
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