A building has an entry the shape of a parabolic arch 74 ft high and 28 ft wide at the base as shown below.
2 answers:
The vertex form of a parabola with coordinates (h, k) is expressed as
y=a(x-h)²+k.
Here, the vertex is positioned at (0,0).
This simplifies to y=a(x-0)²+0, or y=a(x)², leading to y=ax².
Next, we need to determine the value of a.
Observing a specific point (14,-74), we have x=14 and y=-74.
This gives us the equation -74=a(14²).
Thus, we arrive at -74=196a.
Dividing each side by 196 results in a=-37/98.
Therefore, the equation is
y=a(x-h)²+k.
Here, the vertex is positioned at (0,0).
This simplifies to y=a(x-0)²+0, or y=a(x)², leading to y=ax².
Next, we need to determine the value of a.
Observing a specific point (14,-74), we have x=14 and y=-74.
This gives us the equation -74=a(14²).
Thus, we arrive at -74=196a.
Dividing each side by 196 results in a=-37/98.
Therefore, the equation is
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Answer:
Step-by-step explanation:
To determine the slope, divide the rise by the run to calculate the slope.
Note that
1 ft = 12 in
Let
y ----> the rise
x ----> the run
m ----> the slope
the values are given as
substituting these values gives
Simplifying further