Question 1204029
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With the origin halfway between the arch's feet and a maximum height of 30 feet, the vertex of the parabola is (0,30); the equation of the parabola is<br>
{{{y=-ax^2+30}}}.<br>
With a distance of 240 feet between the arch's feet, two points on the parabola are (120,0) and (-120,0).  Use either of those two points to find the coefficient a.<br>
{{{0=-a(120)^2+30}}}
{{{14400a=30}}}
{{{a=30/14400=1/480}}}<br>
ANSWER a: The equation of the parabola is {{{y=-(1/480)x^2+30}}}<br>
Find the height of the arch 107 feet from the center by finding y when x is 107:<br>
{{{-(1/480)(107^2)+30}}} = 6.148 feet to 3 decimal places<br>
ANSWER b: about 6.148 feet<br>