Question

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Explanation:

Step1: Find x-intercepts

To find the x - intercepts, we set \(y = f(x)=0\) and solve for \(x\). We have the equation \(0=(x + 1)(x + 11)\). By the zero - product property, if \(ab = 0\), then either \(a = 0\) or \(b = 0\). So, when \(x+1=0\), we get \(x=-1\); when \(x + 11=0\), we get \(x=-11\).

Step2: Find y-intercept

To find the y - intercept, we set \(x = 0\) in the function \(f(x)=x^{2}+12x + 11\). So, \(f(0)=(0)^{2}+12\times(0)+11=11\).

Answer:

The x - intercepts are \(-1\) and \(-11\). The y - intercept is \(11\).