Identify the axis of symmetry and vertex of f(x) = –2x2 –2x–1.
axis of symmetry: x = – 0.5; vertex: (– 0.5, – 0.50)
axis of symmetry: x = 0.5; vertex: (– 0.5, – 0.50)
axis of symmetry: x = 0.5; vertex: (0.5, – 0.50)
axis of symmetry: x = – 0.5; vertex: (– 0.5, 0.50)

The first option

Step-by-step explanation:

Given a quadratic function in standard form : ax² + bx + c : a ≠ 0, then

The equation of the axis of symmetry which is also the x- coordinate of the vertex is found using

x = -

f(x) = - 2x² - 2x - 1 ← is in standard form

with a = - 2, b = - 2, so

x = - = - 0.5

Equation of axis of symmetry is x = - 0.5

Substitute x = - 0.5 into f(x)

f(- 0.5) = - 2(- 0.5)² - 2(- 0.5) - 1 = - 0.5 + 1 - 1 = - 0.5

Vertex = (- 0.5, - 0.5 )