Question in description

Question

The arch of the Sydney Harbor Bridge in Sidney, Australia, can be modeled by y=-0.00211x^2+1.06x where x is the distance (in meters) from the left pylons and y is the height (in meters) of the arch above the water. The road can be modeled by the equation y=52. To the nearest meter, how far from the left pylons are the two points where the road intersects the arch of the bridge?

Answer 1

So y = 52 = -0.00211 x² + 1.06 x. Subtract 52 from both sides and apply the Quadratic Formula: {-b ±√(b² -4ac)} /2a = {-1.06 ±√[1.06² - 4(-.00211)(-52)]} / (-.00422) yields (-1.06 - 0.827)/2a = 447m and (-1.06 + 0.827)/2a = 55m.