How to find vertex and line of symmetry

Question

f(x)=2x^2-8x+12

Answer 1

If f(x) = ax^2 + bx + c, then the line of symmetry is x = -b/(2a).

For your problem,

x = 8/(2*2) = 2, y = f(2) = 2*2^2 - 8*2+12 = 4

Answer: x = 2, vertex (2, 4)

Attn: The vertex can also be obtained by completing the square.

f(x) = 2(x^2-4x+4) + 4 = 2(x-2)^2 + 4. So, the vertex is at (2, 4). Since the line of symmetry passes through the vertex and is a vertical line, the line of symmetry is x = 2.

Answer 2

2x² - 8x + 12 = 2(x² - 4x + 6)

                   = 2 (x² - 4x + 4 + 2)

                   = 2 ((x - 2)² + 2)

                   = 2 (x - 2)² + 4.

From this, we can tell that the line of symmetry must be x = 2. The 4 at the end means that the vertex is (2, 4); if the number, for example, was 2 instead of 4, the vertex is (2, 2).