Question

The function y=−0.04x2+0.32x+2.5 represents the path of an Olympic swimmer as he enters the pool. x represents the distance, in feet, from the side of the pool and y represents the height of the swimmer, in feet, above the pool. The side of the pool is represented by x=0



Use the quadratic formula to determine how far from the side of the pool the swimmer enters the water.



x=−b±b2−4ac−−−−−−√2a

Answer 1

Answer:

  12.86 feet

Step-by-step explanation:

For quadratic ax² +bx +c = 0, the quadratic formula gives the solutions as ...

  $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

When y=0, your equation has ...

  a = -0.04, b=0.32, c=2.5

so the solutions will be ...

  $x=\dfrac{-0.32\pm\sqrt{0.32^2-4(-0.04)(2.5)}}{2(-0.04)}\\\\=\dfrac{-0.32\pm\sqrt{0.5024}}{-0.08}=4\pm\sqrt{78.5}$

The positive answer is the one of interest:

  x ≈ 12.86 . . . feet

The swimmer enters the water about 12.86 feet from the side of the pool.