Basketball Parabola

Adam Bede

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The picture is of a basketball which is on a shelf in my room

Standard And Vertex Form

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What does the height of the black line represent?

It represents the the maximum value of the parabola, all points have to be inside of the arch and so the y-value can't be a number higher than the y-value in the vertex.

At the spot where the black line goes off the ball, what is the relevance to the equation?

The line goes off the ball in two places and those two places are the roots.

That is the maximum height of the arch?

The maximum height is the y-value in the vertex and that would be 5.

How far away is the beginning of the black line (starting from the left end) when the arch hits its maximum height?

It is the x-value of the vertex which is 4.

What is the domain related to the distance the line is from the spout?

All real numbers

What is the range related to the height of the arch?

0 less than or equal to y less than or equal to 5