Question

The equation h = –0.005x2 + x + 3 describes the path of a baseball hit into the outfield, where h is the height and x is the horizontal distance the ball travels.

a. What is the equation of the axis of symmetry?


b. What is the maximum height reached by the baseball?


c. An outfielder catches the ball three feet above the ground. How far has the ball traveled horizontally when the outfielder catches it?

Answer 1

(a)x=100

(b)Maximum Height, h=53 Units

(c)x=200 Units

Explanation:

Given the equation which describes the path of the baseball

`h = -0.005x^2 + x + 3`

(a)Equation of the axis of symmetry

For a quadratic function of the form
`y=ax^2+bx+c`, its equation of the axis of symmetry is determined by the equation:

`x=-(b)/(2a)`

In the function given: a=–0.005, b=1

Therefore:

`x=-(1)/(2*-0.005)=(1)/(0.01)\\\\x=100`

Equation of the axis of symmetry, x=100

(b)Maximum height reached by the baseball

The maximum height reached by the baseball occurs at the line of symmetry.

Therefore, when x=100

Maximum Height,
`h = -0.005(100)^2 + 100 + 3`

=53 Units

(c)When the height =3 feet, we want to determine the value of x.

`h = -0.005x^2 + x + 3\\3 = -0.005x^2 + x + 3\\-0.005x^2 + x=0\\x(-0.005x + 1)=0\\-0.005x + 1=0\\-0.005x =-1\\$Divide both sides by -0.005\\x=200 Units`