Algebra 2
posted by Alex .
A baseball player swings and hits a pop fly straight up in the air to the catcher. The height of the baseball in meters t seconds after it is hit is given by a quadratic function h(t) = −5t^2 + 10t + 1. What is the maximum height of the baseball?

Method 1: if you know Calculus
h'(t) = 10t + 10 = 0 for a max of h(t)
10t = 10
t = 1
h(1) = 5(1) + 10 + 1 = 6
max height is 6 m when t= 1 second
Method 2: complete the square of the quadratic
h(t) = 5(t^2  2t + ....) + 1
= 5(t^2  2t + 1  1 ) + 1
= 5((t1)^2  1) + 1
= 5(t1)^2 + 6
vertex is (1,6), which tells me the max is 6 when t = 1
method 3:
the x of the vertex is b/(2a) for the general quadratic f(x) = ax^2 + bx + c
so in our case t of vertex = 10/(2(5)) = 1
h(1) = 5(1) + 10(1) + 1 = 6 
Quadratic function:
y = a x ^ 2 + b x + c
has minimum or maximum in point
x =  b / 2 a
If a > 0 quadratic function has minimum
If a < 0 quadratic function has maximum
In your case :
a =  5 , b = 10 , c = 1
Function has maximum in point :
 b / 2 a =  10 / [ 2 * (  5 ) ] = 10 /  10 = 1
h ( max ) = h ( 1 ) =  5 * 1 ^ 2 + 10 * 1 + 1 =
 5 + 10 + 1 = 6 m 
A baseball player swings and hits a pop fly straight up in the air to the catcher. The height of the baseball in meters t seconds after it is hit is given by a quadratic function h(t) = −4.9t^2 + 9.8t + 1. What is the maximum height of the baseball?
Respond to this Question
Similar Questions

Pre Calc
7. The Sandusky Little League uses a baseball throwing machine to help train 10year old players to catch high popups. It throws the baseball straight up with an initial velocity of 48 ft/sec from a height of 3.5 ft. a. Find an equation … 
algebra
Josh hit a baseball straight up into the air. The equation below describes the height of the ball (h), in meters, as a function of time (t) in seconds. h(t) = 9.8t² + 30t + 1.5 
algebra 1
Josh hit a baseball straight up into the air. The equation below describes the height of the ball (h), in meters, as a function of time (t) in seconds. h(t) = 9.8t² + 30t + 1.5 What is the height of the ball after 3 seconds? 
Algebra
A baseball player hits a baseball into the air with an initial vertical velocity of 48 feet per second from a height of 3 feet. 8. Write an equation that gives the baseball’s height as a function of the time (in seconds) after it … 
Alg 1
A baseball player hit a ball with an upward velocity of 46 ft/s. Its height h is feet after t seconds is given by the function h = 16t^2 + 46t + 6. What is the maximum height the ball reaches? 
algebra
in the past professional baseball was played at the astrodome in Houston, Texas. the astrodome has a maximum height of 63.4 m. the height of a baseball t seconds after it is hit straight up in the air with a velocity of 45 ft/s is … 
math
A baseball player swings and hits a pop fly straight up in the air to the catcher. The height of the baseball in meters t seconds after it is hit is given by a quadratic function h(t) = −4.9t^2 + 9.8t + 1. What is the maximum … 
math
A baseball player hits a high popup with an initial upward velocity of 30 m/s, 1.4 m above the ground. The height, h, in metres, of the ball t seconds after being hit is modelled by the function h(t) = 4t^2+30t+1.4. How long does … 
math
The height of a baseball (h) in meters (t) seconds after it has been tossed out a window is given by the equation h= 5t^2 + 20t + 15. A boy shoots at the baseball with a trajectory of h= 3t +3. Will the paintball hit the baseball? 
Algebra
The path of a baseball after being hit is given by the function f(x)= .007x^2+x+4 where f(x) is the height of the baseball (in feet) and x is the horizontal distance from home plate (in feet). at what time will the baseball reach …