Christopher is repairing the roof on a shed. He accidentally dropped a box of nails from a height of 14 feet. This is represented by the equation $h = - 16 t^{2} + 14,$ where $h$ the height in feet and $t$ is the time in seconds. Describe how the graph is related to .

Question

Christopher is repairing the roof on a shed. He accidentally dropped a box of nails from a height of 14 feet. This is represented by the equation $h = - 16 t^{2} + 14,$ where $h$ the height in feet and $t$ is the time in seconds. Describe how the graph is related to .

Accepted Answer

The graph of $h = - 16 t^{2} + 14$ is the graph of $h = t^{2}$ reflected across the $x$ -axis and vertically stretched by a factor 16 and vertically translated 14 units up.

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Christopher is repairing the roof on a shed. He accidentally dropped a box of nails from a height of 14 feet. This is represented by the equation $h = - 16 t^{2} + 14,$ where $h$ the height in feet and $t$ is the time in seconds. Describe how the graph is related to .

Step by Step Solution

Step 1. Define the standard form of the quadratic function.

Step 2. Define the transformations of the graph of the function.

Step 3. Describe how the graph of h=−16t2+14 is related to the graph of h=t2.

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Algebra 1

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Christopher is repairing the roof on a shed. He accidentally dropped a box of nails from a height of 14 feet. This is represented by the equation h=−16t2+14, where h the height in feet and t is the time in seconds. Describe how the graph is related to .

Step by Step Solution

Step 1. Define the standard form of the quadratic function.

Step 2. Define the transformations of the graph of the function.

Step 3. Describe how the graph of h=−16t2+14 is related to the graph of h=t2.

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Christopher is repairing the roof on a shed. He accidentally dropped a box of nails from a height of 14 feet. This is represented by the equation $h = - 16 t^{2} + 14,$ where $h$ the height in feet and $t$ is the time in seconds. Describe how the graph is related to .