Using a Parabola: Maximum Height Reached by a Soccer Ball

If a soccer ball is kicked straight up from the ground with an initial velocity of 32 feet per second, then its height above the earth in feet is given by s(t) = -16t^2 + 32t where t is time in seconds. Graph this parabola for 0 < or equal to t < or equal to 2. What is the maximum height reached by the ball?

Solution Summary

This solution provides a step-wise response, which includes a figure, to illustrate how to find the maximum height of a soccer ball using the vertex of a parabola. This is all presented in an attached Word document.

Word Problem
Diagonal Brace: The width of a rectangular gate is 2 meters (m) larger than its height. The diagonal brace measures √6m. Find the width and height.
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Graph each parabola.
y = -1/3*(x^2) + 5
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Find the vertex and intercept for each parabola.
g(x) = x^2 +x-6
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Foul ball. Suppose Charlie O'Brien hits a baseball straight upward at 150 ft/sec from a height of 5 ft.
Use the formula to determine how long it takes the ball to return to the earth.
Use the graph to estimate the maximumheightreached by the ball. See attachment.

Need help with attached word problems (see attachment for full details)
1. During the championship soccer game, the goalkeeper, Brandon,
kicked the ball straight up to the Mid-Fielder, Alex, with an initial velocity of 32 feet per second. The height of the ball relative to the ground is a function of time given by the

The path traveled by a golf ball hit with a 9-iron can be modeled with quadratic function, y= -0.042X 2 + 5X, where x is the distance in yards from the point it was hit and y is the height of the golf ball in feet. Assume that the ground is level.
A. Find the maximumheightreached by the ball.
B. How far from where it was

A battalion of soldiers aims their cannon at an angle of 30° up from horizontal and fires it as shown below in a large, level field. The initial speed of the cannon ball is 196 m/s. Neglect air resistance and assume that the cannon ball starts at ground level for simplicity. Use g = 9.8 m/s2. What is the maximumheight reac

If a baseball is projected upward from ground level with an initial velocity of 64 feet per second, then its height is a function of time, given by s(t) = -16t squared + 64t. How would I graph this function for 0 ≤ t ≤ 4? And how do I determine the maximumheightreached by the ball?

The parabola y = (x^2) + 3 has two tangents which pass through the point (0, -2). One is tangent to the to the parabola at (A, A^2 + 3) and the other at (-A, A^2 + 3). Find (the positive number) ?
If a ball is thrown vertically upward from the roof of 64ft foot building with a velocity of 96 ft/sec, its height after t seconds

If a ball is thrown vertically upward from the roof of a 48 foot building with a velocity of 64ft/sec, its height after t seconds is s(t)=48 + 64t -16t^2. What is the maximumheight the ball reaches?
What is the velocity of the ball when it hits the ground (height 0)?

Could you help me?
A ball is thrown vertically upwards with an initial speed of 40m/s
a) What is the value of the instantaneous speed and the acceleration when the ball reaches its maximumheight?
b) How long does it take to reach this height?
c) How long does it take the ball to fall from the maximumheight to the o