# The St Louis Gateway is an arc, which is a curve, that approximates a parabola. The arc is 192m wide and 192m tall. a)Label the x-intercepts and the vertex. b) Determine the equation to model...

The St Louis Gateway is an arc, which is a curve, that approximates a parabola. The arc is 192m wide and 192m tall.

a)Label the x-intercepts and the vertex.

b) Determine the equation to model the arc

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### 1 Answer

(1) Let (0,0) be the foot of one of the sides. Then since the base is 192m wide, the other foot is at (192,0).

(2) The arch models a parabola opening down, so the vertex is the highest point. Also, the vertex lies on the axis of symmetry, which is midway between the zeros. Thus the highest point, the vertex, is at (96,192).

(3) The vertex form of a parabola is `y=a(x-h)^2+k` where `h` and `k` are the coordinates of the vertex, and `a` determines if the parabola opens up/down, and how wide.

Here, `y=a(x-96)^2+192` . We can use another point on the parabola to determine `a` . Choose to use (0,0).

Then at (0,0) `0=a(0-96)^2+192=>9216a=-192=>a~~-.02`

**Thus the zeros are at (0,0) and (192,0); the vertex is at (96,192); and the equation is `y=(-12)/(601)(x-96)^2+192` or approximately `y=-.02(x-96)^2+192` **