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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.
f(x) = -x2 - 6x

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xKelvin xKelvin · Answer 1 · 2021-06-15T05:31:59+02:00

Answer:

The vertex is at (-3, 9).

The axis of symmetry is x = -3.

Step-by-step explanation:

We have the function:

[tex]f(x)=-x^2-6x[/tex]

And we want to determine its vertex and the equation of its axis of symmetry.

The vertex can be found with the following formulas:

[tex]\displaystyle \text{Vertex}=\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]

In this case, a = -1, b = -6, and c = 0.

Find the x-coordinate of the vertex:

[tex]\displaystyle x=-\frac{(-6)}{2(-1)}=-3[/tex]

To find the y-coordinate substitute this value back into the function:

[tex]\displaystyle f\left(-\frac{b}{2a}\right)=f(-3)=-(-3)^2-6(-3)=9[/tex]

So, the vertex of the equation is (-3, 9).

The axis of symmetry is goes through the vertex point. So, the equation for the axis of symmetry is simply the x-value. Therefore, the equation is:

[tex]x=-3[/tex]

Rashmeetkaur45 Rashmeetkaur45 · Answer 2 · 2021-06-15T05:33:01+02:00

Step-by-step explanation:

you can arrange 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 symmetry then lies in x =-1.5

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