SOLUTION: When a ball is thrown or kicked, the path it travels is shaped like a parabola. Suppose a football is kicked from ground level, reaches a maximum height of 20 feet, and hits the gr

Question 1195875: When a ball is thrown or kicked, the path it travels is shaped like a parabola. Suppose a football is kicked from ground level, reaches a maximum height of 20 feet, and hits the ground 120 feet from where it was kicked. Assuming that the ball was kicked at the origin, write an equation of the parabola that models the flight of the ball.

Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
When a ball is thrown or kicked, the path it travels is shaped like a parabola. Suppose a football is kicked from ground level, reaches a maximum height of 20 feet, and hits the ground 120 feet from where it was kicked. Assuming that the ball was kicked at the origin, write an equation of the parabola that models the flight of the ball.
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y = ax^2 + bx + c
3 points are given: (0,0), (60,20) and (120,0)
Can you do the rest?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Finding the equation using standard form and using the three known points to form a system of three equations in a, b, and c is one way to get the answer.

Usually an easier way, when the vertex of the parabola is known, is to use the vertex form of the equation of a parabola:

Knowing the points (0,0), (60,20), and (120,0), we know the vertex is (60,20). So

Use either of the other two points to determine the constant a. Using (0,0)...

ANSWER:

Then manipulate that equation to put it in the required form, if necessary.

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