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The main cable of a suspension bridge forms a parabola, described by the equation [tex] y = a(x - h)^2 + k [/tex].

- [tex] y [/tex] = height in feet of the cable above the roadway
- [tex] x [/tex] = horizontal distance in feet from the left bridge support
- [tex] a [/tex] = a constant
- [tex] (h, k) [/tex] = vertex of the parabola

What is the vertex of the parabola?

Sagot :

GinnyAnswer
To find the vertex of the parabola described by the equation [tex]\( y = a(x - h)^2 + k \)[/tex], let's analyze the components of the vertex form of the equation.

The equation [tex]\( y = a(x - h)^2 + k \)[/tex] represents a parabola that opens either upwards or downwards, depending on the sign of the constant [tex]\( a \)[/tex].

In the vertex form of a parabola:
- [tex]\( h \)[/tex] represents the x-coordinate of the vertex.
- [tex]\( k \)[/tex] represents the y-coordinate of the vertex.

Therefore:
[tex]\[ (h, k) \][/tex]
are already given as parts of the equation.

Thus, the vertex of the parabola is:
[tex]\[ \boxed{(h, k)} \][/tex]
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