Question 1013457
 a parabolic arch has a width of 18 m across the bottom.
 at a vertical distance 3 m above the bottom, the width across the arch is 12 m. what is the height of the arch in meters?
:
Using the form ax^2 + bx + c = y
arch will be going thru origin, 0,0 so c = 0
Using two pairs; x=3; y=3 and x=15, y=3, construct two equations
x=3; y=3
9a + 3b = 3
Simplify,divide by 3
3a + b = 1
b = (-3a+1)
:
x=15; y=3
225a + 15b = 3
simplify, divide b 3
 75a + 5b = 1
Replace b with (-3a+1)
75a + 5(-3a+1) = 1
75a - 15a + 5 = 1
60a = 1 - 5
a = -4/60
a = -.0667
Find b using b = -3a+1
b = -3(-.0667) + 1
b = .2 + 1
b = 1.2
:
The equation for our arch: y = -.0667x^2 + 1.2x
:
Looks like this, green line is y = 3
{{{ graph( 300, 200, -6, 25, -8, 16, -.0667x^2+1.2x, 3) }}}
Axis of symmetry x=9
Find max, the height of the arch
y = -.0667(9^2) + 1.2(9)
y = -5.4 + 10.8
y = 5.4 meters is the height of the arch