What is the axis of symmetry for f(x) = 2x² + 4x + 2?

Solution:

Given, the function is f(x) = 2x² + 4x + 2 ---------- (1)

We have to identify the axis of symmetry of the function.

The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves. The axis of symmetry always passes through the vertex of the parabola.

The equation of the parabola in quadratic form is given by

y = ax² + bx + c ------------ (2)

The vertex is (h, k)

where h = -b/2a and k = (4ac - b²)/4a.

Comparing (1) and (2)

a = 2

b = 4

c = 2

So, h = -4/2(2)

= -4/4

h = -1

4ac = 4(2)(2)

4ac = 16

So, k = [16 - (4)²]/4(2)

k = (16 - 16)/(8)

k = (0)/8

k = 0

Thus, (h, k) = (-1, 0)

x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.

So, the axis of symmetry is x = -1

Therefore, the axis of symmetry is x = -1.