d)) Find \( g(x) \), where \( g(x) \) is the translation 4 units left of \( f(x)=x^{2} \). \( g(x)= \) Write your answer in the form \( \mathrm{a}(\mathrm{x}-\mathrm{h})^{2}+\mathrm{k} \), where a , h , and k are integers. (D)
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To translate the function \( f(x) = x^{2} \) 4 units to the left, you need to replace \( x \) with \( x + 4 \). This gives you: \[ g(x) = (x + 4)^{2}. \] Next, we can express this in the desired form \( a(x - h)^{2} + k \). By expanding \( (x + 4)^{2} \), we get: \[ g(x) = x^{2} + 8x + 16. \] In this case, let’s rewrite it as: \[ g(x) = 1(x - (-4))^{2} + 0. \] Thus, \( g(x) = 1(x + 4)^{2} + 0 \), where \( a = 1 \), \( h = -4 \), and \( k = 0 \). The final answer is: \[ g(x) = (x + 4)^{2}. \]
