# Lesson 2 Root Variation Solidify Understanding

A team of astronomers have been studying the paths of specific objects in the night sky by graphing them in a coordinate plane. The origin represents midnight. The

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Use Dr. Stella’s method for problems 3 and 4.

One astronomer, Dr. Stella, wrote a system of two equations to see if she could predict when the paths of the objects she was studying would intersect.

She solved the system by setting the equations equal to each other and solving for

After solving the systems, she looked at the graphs of the equations to check if she was right.

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Set the equations equal to each other and solve for

Check your answer by graphing.

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Set the equations equal to each other and solve for

Check your answers by graphing.

The square root function

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Find the speed of an object in free fall after it has fallen

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Find the speed of an object in free fall after it has fallen

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The table shows the speed of the object during the first

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At how many seconds will the object’s speed double again?

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At how many seconds will the object’s speed double a third time?

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If an object in free fall is moving at a speed of

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If an object in free fall is moving at a speed of

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Graph

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Two graphs are shown on the same grid. Both graphs show a proportional relationship. In one, the output quantity varies directly with the input quantity. In the other, the output quantity varies directly with the square root of the input quantity. Write the equations for each graph.

Find each product.

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What is the square root of

Find the square root.