Question

A building has an entry the shape of a parabolic arch 74 ft high and 28 ft wide at the base as shown below.

A parabola opening down with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is seventy four feet and its width from left to right is twenty eight feet.

Find an equation for the parabola if the vertex is put at the origin of the coordinate system.

Answer 1

If a building has an entry shape of a parabolic arch 74 ft high and 28 ft wide at the base as shown in the figure and then the vertex is at (0,0). The parabola is opening downward, so the equation to be used is x² = -4ay. 4a is equal to 28 and so the equation is x² = -28y

Answer 2

the equation of a parabola with vertex at (h,k) is
y=a(x-h)²+k

vertex isi at (0,0)

y=a(x-0)²+0
y=a(x)²
y=ax²
find a

we see that one point is (14,-74)
x=14 and y=-74

-74=a(14²)
-74=196a
divide both sides by 196
-37/98=a

the equation is


`y= (-37)/(98) x^2`