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Explain the transformations that change the function \(f(x) = x^2 \) into \(h(x) = 24 - 4x^2 \).
Multiplication by \(a\) is always first. In this case, \(f(x)\) is multiplied by \(-4\) to make \(g(x) = -4x^2\). Next, \(p\) and \(q\) are applied. For this function, \(q = 24\) and \(p = 0\). Therefore, \(g(x) = -4x^2 \) is translated up \(24\) units to make \(h(x) = -4x^2 + 24 \).