QUESTION 1 Find the \( y \)-and \( x \)-intercepts of \( f(x)=2(x-4)(x+1)^{2}(x-6) \) Write each one as an ordered pair, such as \( (0,5) \) or \( (10,0) \) The \( y \)-intercept is The \( x \)-intercepts are Note: Enter your \( x \)-intercepts from smallest to largest and DO NOT USES SPACES. Ex: \( (-1,0),(0,0),(3,0) \)

To find the \( y \)-intercept, substitute \( x = 0 \) into the function: \[ f(0)=2(0-4)(0+1)^2(0-6) = 2(-4)(1)(-6) = 48 \] Thus, the \( y \)-intercept is \( (0,48) \). Now, for the \( x \)-intercepts, we set \( f(x) = 0 \): \[ 2(x-4)(x+1)^{2}(x-6) = 0 \] The roots are found by setting each factor to zero: 1. \( x - 4 = 0 \) gives \( x = 4 \) 2. \( x + 1 = 0 \) gives \( x = -1 \) (with multiplicity 2, but only counts as one intercept for distinct values) 3. \( x - 6 = 0 \) gives \( x = 6 \) Thus, the \( x \)-intercepts are \( (-1,0),(4,0),(6,0) \).