SOLUTION: A building has an entry the shape of a parabolic arch 74 ft high and 28 ft wide at the base, as sgown below. A parabola opening down with vertex at the origin is graphed on the

Question 1027923: A building has an entry the shape of a parabolic arch 74 ft high and 28 ft wide at the base, as sgown 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.

Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
The description expresses three points which you can use for a standard form equation. The vertex is stated to be (0,0) and is a maximum; two other points are (-14,-74) and (14,-74).
Think how that makes sense before continuing...

...

Simplifies to and you simply need to use one of the points to determine the value for a.
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

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

Vertex: (0, 74) =====> (h, k)
Roots: (- 14, 0) and (14, 0) ====> and
Equation for vertex form of a parabola:
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