Final answer:
To find the axis of symmetry for f(x) = x² + 16x + 8, use x = -b/(2a), resulting in x = -8. The vertex of this parabola is (-8, -56).
Step-by-step explanation:
The question pertains to finding the axis of symmetry for the given quadratic function f(x) = x² + 16x + 8. To find the axis of symmetry for a parabolic equation of the form y = ax² + bx + c, we use the formula x = -b/(2a). For the given quadratic function, where a = 1 and b = 16, the axis of symmetry is x = -16/(2×1) = -8.
The vertex of the parabola, which lies on the axis of symmetry, will have the x-coordinate of -8. To find the y-coordinate of the vertex, we substitute x = -8 into the original equation: f(-8) = (-8)² + 16(-8) + 8, resulting in f(-8) = 64 - 128 + 8, and thus f(-8) = -56. Therefore, the vertex of the parabola is at the point (-8, -56). Knowing the vertex and the axis of symmetry allows for a complete understanding of the parabolic shape and informs predictions about the function's graph.