Question

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)=4x^2+5x+2

Answer 1

• vertex: (-5/8, 7/16)
• axis of symmetry: x = -5/8

Explanation:

For quadratic ax²+bx+c, the axis of symmetry is located at x=-b/(2a).

Here, we have a=4, b=5, so the axis of symmetry is ...

... x = -5/(2·4) = -5/8

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The vertex y-value will be f(-5/8).

... f(-5/8) = (4·(-5/8) +5)·(-5/8) +2 = (5/2)·(-5/8) +2 = -25/16 +32/16

... f(-5/8) = 7/16

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The axis of symmetry is x = -5/8; the vertex is (-5/8, 7/16).