The arch support of a bridge can be modeled by y=-0.0012x^2 where x and y are measured in feet. Find the height and width of the arch.
I don't know how to even attempt to solve this... If you know how, can you PLEASE help asap!!
height: 300 feet
width: 1000 feet
WIDTH: 342941 :HEIGHT: 243143
To find the height and width of the arch, we can use the equation provided: y = -0.0012x^2. In this equation, y represents the height of the arch at a given point x.
To find the height, we need to find the maximum point on the graph since the height of the arch is at its peak. The maximum point of a parabola occurs at the vertex. The x-coordinate of the vertex can be found using the formula: x = -b/2a. In our case, a = -0.0012 and b = 0.
Substituting these values into the formula, we calculate: x = -0/2(-0.0012) = 0.
Now we substitute this x-coordinate back into the original equation to find the height (y) at x = 0: y = -0.0012(0)^2 = 0.
Therefore, the height of the arch is 0 feet.
To find the width of the arch, we need to determine the points where the height (y) equals zero. This occurs when the equation -0.0012x^2 = 0. Taking out common factors, we have x^2 = 0.
This implies that x = 0.
Hence, the width of the arch is also 0 feet.
Therefore, based on the given equation, the arch has no height or width as it is a straight line at ground level.
This cannot be right, as the vertex is at (0,0)
You need an equation of the form
y = a - bx^2
where the height of the arch is at a, and the width is 2√(a/b)