A geometry textbook gives the equation of a parabola as y =x^2, where x
and y are measured in inches. How can this equation be dimensionally correct? how I will answer this thanks
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I think that if \(x\) is measured with \(inches\), then \(y\) has to be measured with \(inches^2\)
Here we're discussing the equation of a parabola in cartesian coordinates. The graph of a parabola is the collection of points that satisfy the equation y=x^2. The point (2,3) would be located 2 units to the right of the y-axis, and 3 units up from the x-axis. There's no reason why the variable (distance) y should have units of "square inches."
In other contexts, "square inches" would be appropriate. For example, suppose that x is the length of a side of a square. The area of the square would be A=x^2, measured in "square inches."