Tennis-ball Parabola

Kennedy And Nathan

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Vertex, Roots, Standard and Vertex form

The vertex of the tennis ball is: (3.5ft,3ft)

Two points are: (0ft,0ft) and (7.5ft,0ft)


The standard form is: y=-12/49x^2-7x+61/4

The vertex form is: y=-12/49(x-3(1/2))^2+3

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The x-axis represents the distance of the ball and the y-axis represents the height of the ball. Both the height and the distance are measured in feet.

Questions

1. What does the height of the tennis ball leaving the ground represent? The height of the tennis ball leaving the ground represents the y-intercept, where the ball crosses the y-axis.

2. At the spot where the tennis ball hits the ground the second time, what is the relevance to the equation? It is used as a second root, meaning landing on the x-axis. The second root is (7.5,0)

3. What is the maximum height of the tennis ball? 3 feet

4. How far away is the tennis ball when it reaches it's maximum height? 3.5 feet

5. What is the domain related to the distance of the tennis ball? 0<_x<_7.5

6. What is the range related to the height of the tennis ball? Y<_3