Question 1203474
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The two responses you have received to this point show variations of a standard formal algebraic solution.<br>
Here is a different, informal method which can sometimes make solving problems like this easier (and sometimes not!)<br>
Since the shape is a parabola, the change in the y value from the axis of symmetry is proportional to the square of the corresponding change in the x value.<br>
The height of the arch is on the axis of symmetry, which we can consider to be x=0.<br>
Let h be the height of the arch -- i.e., the vertex of the parabola is at (0,h).  The point (1,8) on the arch is 1 unit horizontally and (h-8) units vertically from the top of the arch; the point (10,0) is 10 units horizontally and h units vertically from the top of the arch.<br>
The second point is 10 times as far from the axis of symmetry as the first, so the difference in the vertical distance from 0 to the top of the arch should be 100 times the difference in the vertical distance from (1,8) to the top of the arch:<br>
{{{h=100(h-8)}}}
{{{h=100h-800}}}
{{{99h=800}}}
{{{h800/99}}} = 8.0808...<br>
ANSWER: The height of the arch is 8.08 feet, to 2 decimal places.<br>