Question

A parabolic arch has a 100 meter base and height of 25 meter. Find the height of the arch at the point 30 meter from the centre of the base.

Answer 1

is this pre calc?

Answer 2

Analytical Geometry

Answer 3

write the parabola in vertex from
the vertex is at (0,25) and the parabola opens downwards so we have

y = -a(x - b)^2 + c where (b,c) is the vertex

y = -a(x - 0)^2 + 25

Answer 4

negative a because it opens downwards

Answer 5

Find a by plugging in another point on the graph ( 50,0) so you can complete the equation of the parabola.

Then find the required height by plugging in x = 30 and finding y.

Answer 6

ok?

Answer 7

Okay thanks.

Answer 8

yw