An arch is in the shape of a parabola. it has a span of 100 feet and a maximum height of 25 ft.
find the equation of the parabola, and use that to determine the height of the arch 10 feet from the center. round to 2 decimal places.

the height of the arch 10 feet from the center is 24 feet

Step-by-step explanation:

An arch is in the shape of a parabola. It has a span of 100 feet, the vertex lies at the center 50 and the maximum height of 25 ft.

Vertex at (50,25)

vertex form of the equation is

, (h,k) is the center

the parabola starts at (0,0) that is (x,y)

subtract 25 from both sides

divide both sides by 2500

the height of the arch 10 feet from the center.

center is at 50, 10 feet from the center so x=40 and x=60

y=24

the height of the arch 10 feet from the center is 24 feet

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: