A building has an entry the shape of a parabolic arch 96 ft high and 18 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 ninety six feet and its width from left to right is eighteen feet.

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

Question

A building has an entry the shape of a parabolic arch 96 ft high and 18 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 ninety six feet and its width from left to right is eighteen feet. 

Find an equation for the parabola if the vertex is put at the origin of the coordinate system.

anonymous · Answer

above figure describes your question.. 

A DOWNWARD OPENING PARABOLA OF MENTIONED DIMENSIONS. SUCH PARABOLAS HAVE THE EQUATIONS IN THE FORMAT 
$$X ^{2}=-4aY$$

Now, right-bottom point of the parabola has the coordinates (9,96). So, put X=9 and Y=96 .. and get the value of 4a= 27/32

Now, put the value of 4a to get the equation of parabola as, 

$$32X ^{2}=-27Y$$


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