Question 622222: If an arch is 100 m wide at its base and 100 m high in the middle, find the quadratic relation, in standard form, that models this shape.
Answer by matineesuxxx(27)   (Show Source):
You can put this solution on YOUR website! the first thing to notice is that we need to start using the factored form of a quadratic, and this would leave us with:
 where s and r are the zeros.
now since this arch is 100 meters wide, we can use either zeros that are x= 0 , 100 or x=-50 , 50..
the fact of the matter is that is doesnt matter, as long as the sum of the absolute values of s and r add up to 100. lets use zeros of x=0 and x=100.
next thing is to find the vertex of the parabola. well to find the vertex with the zeros, you add the zeros and divide by two. this is because the vertex is exactly in the middle between the zeros. so,
 so the x coordinate of the vertex is 50, we also are given that it is 100 meters high at the middle, so we know the vertex is (50,100)
now plug this point into our factored form equation and solve for 'a'
now we have an equation in factored form written as,
now expand (multiply -x/25 into the brackets) and you get:
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