Question

question
factor to find all x-intercepts of the function.
$f(x) = -x^2 - 6x - 8$
answer attempt 2 out of 2
additional solution no solution
$x = -x^2 - 6x - 8$
this is the only question in this section.

Explanation:

Step1: Factor out -1

First, factor out -1 from the quadratic function \( f(x) = -x^2 - 6x - 8 \) to make the quadratic coefficient positive. We get \( f(x) = - (x^2 + 6x + 8) \).

Step2: Factor the quadratic

Now, factor the quadratic \( x^2 + 6x + 8 \). We need two numbers that multiply to 8 and add up to 6. Those numbers are 2 and 4. So, \( x^2 + 6x + 8 = (x + 2)(x + 4) \).

Step3: Write the factored form

Substituting back, we have \( f(x) = - (x + 2)(x + 4) \).

Step4: Find x-intercepts

To find the x-intercepts, set \( f(x) = 0 \). So, \( - (x + 2)(x + 4) = 0 \). This implies \( (x + 2)(x + 4) = 0 \) (since -1 ≠ 0). Setting each factor equal to zero: \( x + 2 = 0 \) gives \( x = -2 \), and \( x + 4 = 0 \) gives \( x = -4 \).

Answer:

The x - intercepts of the function \( f(x)=-x^{2}-6x - 8 \) are \( x=-2 \) and \( x=-4 \).