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The surface of a road curves like a parabola to allow water to drain off of it. The given equation shows the surface height,
y, in feet above the base at a point
x feet from the left edge of the road.

y=-0.0015 x(x-40)
The base has the same width as the road. What is the width of the road in feet?

The surface of a road curves like a parabola to allow water to drain off of it. The given equation shows the surface height, $y$ , in feet above the base at a point $x$ feet from the left edge of the road. $\newline$ $y=-0.0015 x(x-40)$ $\newline$ The base has the same width as the road. What is the width of the road in feet?

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Scale drawings: word problems

Full solution

Q. The surface of a road curves like a parabola to allow water to drain off of it. The given equation shows the surface height,

y

, in feet above the base at a point

x

feet from the left edge of the road.

\newline

y=-0.0015 x(x-40)

\newline

The base has the same width as the road. What is the width of the road in feet?

Identify x-intercepts: Identify the x-intercepts of the parabola to determine the width of the road. $\newline$ The equation of the parabola is given by $y = -0.0015 x(x - 40)$ . The x-intercepts occur when $y = 0$ . $\newline$ $0 = -0.0015 x(x - 40)$
Solve equation for x: Solve the equation for $x$ to find the $x$ -intercepts. $\newline$ We can factor out $x$ from the equation: $\newline$ $0 = x(-0.0015 x + 0.0015 \times 40)$ $\newline$ $0 = x(-0.0015 x + 0.06)$ $\newline$ The $x$ -intercepts are $x = 0$ and $x = 40$ .
Determine road width: Determine the width of the road using the x-intercepts. $\newline$ The width of the road is the distance between the two x-intercepts. Since the x-intercepts are $0$ and $40$ , the width of the road is $40$ feet.

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