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A bridge forms a parabolic arch. The span of the arch is 80 meters and its centre is 15 meters above either end. Write a quadratic equation that models the arch.

dfeuer
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Steve dumonski
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1 Answers1

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Envision the arch as symmetrical about the y-axis. Then the $y$ coordinate of the center is given by $y = 15$.

Since's its span (at its base) is $80$ meters, and parabolas are symmetric about their axes, the axis here being the line $x = 0$, the vertex of the parabola is given by $(0, 15)$.

The base "ends" will each be located $40$ meters from the origin in each direction, thus intersecting the x-axis at the points $(-40, 0),$ and $(40, 0)$.

Now, our arch opens downwards. Now use the general formula for a parabola, $$(y - y_0) = 2a(x - x_0)^2$$ where $(x_0, y_0)$ is the vertex of the parabola, the value of $a$ will be negative, and you can use either of your two points on the parabola to solve for $a$.

amWhy
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