Question

what is the axis of symmetry of the graph of the function f(x)=-x^2 - 6x + 8? a. x = 8 b. x = 3 c. x=-6 d. x=-3

Explanation:

Step1: Recall axis - of - symmetry formula

For a quadratic function \(y = ax^{2}+bx + c\), the axis of symmetry is given by \(x=-\frac{b}{2a}\).

Step2: Identify \(a\) and \(b\) values

In the function \(f(x)=-x^{2}-6x + 8\), \(a=-1\) and \(b=-6\).

Step3: Calculate the axis of symmetry

Substitute \(a=-1\) and \(b = - 6\) into the formula \(x=-\frac{b}{2a}\), we get \(x=-\frac{-6}{2\times(-1)}=-\frac{-6}{-2}=-3\).

Answer:

D. \(x=-3\)