SOLUTION: 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.

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:
}
RELATED QUESTIONS
An engineer is designing a parabolic arch. The arch must be 15 m high and 6 m wide at a... (answered by ankor@dixie-net.com)

The Rainbow Bridge is Utah, is a natural arch that is approximately parabolic in shape.... (answered by Fombitz)

Hi, tutor. Can you please help me solve the following word problem. A parabolic arch... (answered by lynnlo)

A parabolic arch supports a bridge. The arch is 200 m wide at its base and 4 m tall in... (answered by josgarithmetic)

A bridge uses a parabolic arch to support it as shown in the picture. The bridge is 100 m (answered by galactus)

an engineer is designing a parabolic arch must be 15 m high and 6 m wide at a height of... (answered by solver91311)

To accommodate the road beneath, the arch is 100 feet wide at its base, 20 feet high in... (answered by scott8148)

*PLEASE HELP* The water fountain arch reaches 14 feet high and is 28 feet wide at the... (answered by solver91311)