The arch of the gateshead millennium bridge forms a parabola with equation:
y= -0.016(x-52.5)²+45
where x is the horizontal distance (in meters) from the arch’s left end and y is the distance (in meters) from the base of the arch. what is the width of the arch?

  about 106 meters

Step-by-step explanation:

The difference in x-values when y=0 is found by solving ...

  0 = -0.016(x -52.5)² +45

  -45 = -0.016(x -52.5)² . . . . . . subtract 45

  45/0.016 = (x -52.5)² . . . . . . . divide by the coefficient of the squared term

  ±√2812.5 = x -52.5 . . . . . . . . take the square root

  x = 52.5 ±√2812.5 . . . . . . . . .add 52.5. These are the x-values where y=0.

So, the difference in x-values at y=0 is ...

  (52.5 +√( )) - (52.5 -√( )) = 2√2812.5 ≈ 106.07 . . . . meters

The width of the arch at ground level is about 106 meters.

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0