Question

Given the equation f(x) = (x + 3)2 – 8, fill in the blanks:

Axis of symmetry: x =

Vertex:( , )

Number of real solutions:

Answer 1

Quadratic f(x) = (x -h)² +k has vertex (h, k) and axis of symmetry x=h. When k is negative, the number of real solutions is 2, because both branches of the function cross the x-axis.

In your equation, h = -3 and k = -8.

Axis of symmetry: x = -3
Vertex: (-3, -8)
Number of real solutions: 2