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To write a quadratic function in standard form with integral coefficients and a double root of x, we can use the fact that a double root means that the quadratic function has one repeated root. This implies that the quadratic function can be written as (x - r)^2, where r is the repeated root. Expanding this expression will give us a quadratic function in standard form.
Let's demonstrate this with an example:
Given the double root of x = 2, the quadratic function would be:
y = (x - 2)^2
Expanding this expression:
y = (x - 2)(x - 2)
y = x^2 - 2x - 2x + 4
y = x^2 - 4x + 4
Therefore, the quadratic function in standard form with integral coefficients and a double root of x = 2 is:
y = x^2 - 4x + 4