# A building has an entry the shape of a parabolic arch 84 ft high and 42 ft wide at the base as shown below. Find an equation for the parabola if the vertex is put at the origin of the coordinate system.

QUESTION POSTED AT 01/06/2020 - 03:37 PM

QUESTION POSTED AT 01/06/2020 - 03:37 PM

**Answer:**

**Step-by-step explanation:**

A building has an entry the shape of a parabolic arch 84 ft high and 42 ft wide

Since we are given that it is 42 ft wide So, 21 feet from line of symmetry to either end at the base.

Since the vertex is located at origin .

So, equation of parabola =

Since arch is 84 feet high and 42 feet wide, parabola will go through points located 84 units down and 21 units to the left and right : (-21,-84), (21, -84)

So,equation of given parabolic building is :

Substitute the point (-21,-84)

Substitute the value of a in the equation:

**Hence an equation for the parabola if the vertex is put at the origin of the coordinate system is **

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