Question

y=−0.04x2+0.32x+2.5
y
=
-
0
.
04
x
2
+
0
.
32
x
+
2
.
5
represents the path of an Olympic swimmer as he enters the pool. x
x
represents the distance, in feet, from the side of the pool and y
y
represents the height of the swimmer, in feet, above the pool. The side of the pool is represented by x=0

Answer 1

Answer:

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

Step-by-step explanation:

The correct question is

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.

we have

$y=-0.04x^2+0.32x+2.5$

we know that

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$y=-0.04x^2+0.32x+2.5$

Equate the quadratic equation to zero

$-0.04x^2+0.32x+2.5=0$

so

$a=-0.04\\b=0.32\\c=2.5$

substitute in the formula

$x=\frac{-0.32\pm\sqrt{0.32^{2}-4(-0.04)(2.5)}} {2(-0.04)}$

$x=\frac{-0.32\pm\sqrt{0.5024}} {-0.08}$

$x=\frac{-0.32+\sqrt{0.5024}} {-0.08}=-4.86$

$x=\frac{-0.32-\sqrt{0.5024}} {-0.08}=12.86$

therefore

The solution is x=12.86 ft