Word Problems: Dealing with Maximum

[Tigertigre2000]

A Baseball is hit 3 feet above ground at a velocity of 100 feet per second and at an angle of 45 degrees with respect to level ground. The path of the baseball is given by the function f(x) = -.0032x^2 +x+3, where f(x) is the height of the baseball (in feet) and x is the distance from home plate (in feet). What is the maximum height reached by the baseball?

My thought : How do you determine which is the "maximum height"?

 

[stapel]

f(x) = -.0032x^2 +x+3

How do you determine which is the "maximum height"?

You find the vertex of the given quadratic.

Eliz.

 

[skeeter]

f(x) = -.0032x^2 +x+3

the height function is a quadratic, whose graph is a parabola ... since the leading coefficient is negative, the parabola opens down. this means that the maximum height occurs at the vertex of the parabola.

first, find the x-coordinate of the vertex by evaluating the expression -b/(2a)
{note: you do know what a and b represent, correct?}

second, use that x-coordinate for the vertex to determine f(x), which will give you the max height.

you should get a max height a little over 81 ft.