Q: How does graph of y equals x square-1 different from the graph of y equals x square plus 7?

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Yes, that is a shifted tanX graph, just as you would shift any graft.

There needs to be an x variable to create a graph.

If x equals a constant number, the graph will be a vertical line. For example, the graph of x = 5 would be a vertical line that goes through the point (5,0). x equals 5 on every point along this lines.

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first lets find the square feet in one square. 2 feet by 2 fee = 4 square feet per square on a graph. Then you want four of those so 16 square feet in four 2x2 foot squares

No translation will invert a quadratic graph.

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The highest point on a graph is when the derivative of the graph equals 0 or the slope is constant.

Any graph with the slope of -1/2

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The slope or gradient is the same and would run parallel but the intercept on the y axis would be at -1

Yes, that is a shifted tanX graph, just as you would shift any graft.

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You are describing a circle, with its center at the origin and a radius of 4 (the square root of 16)

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There needs to be an x variable to create a graph.