X^2-4x+2=0 convert from standard form to vertex form and identify vertex and axis of symmetry.

Standard Form to Vertex Form

y = x² - 4x + 2

y - 2 = x² - 4x

y - 2 + 4 = x² - 4x + 4

y + 2 = (x - 2) (x - 2)

y + 2 = (x - 2) ²

y = (x - 2) ² - 2

Vertex

y = x² - 4x + 2 = 0

x² - 4x + 2 = 0

x = - (-4) + / - √ ((-4) ² - 4 (1) (2))

2 (1)

x = 4 + / - √ (16 - 8)

2

x = 4 + / - √ (8)

2

x = 4 + / - 2.83

2

x = 2 + / - 1.415

x = 2 + 1.415 x = 2 - 1.415

x = 3.145 x = 0.585

y = x² - 4x + 2

y = (3.145) ² - 4 (3.145) + 2

y = 9.891025 - 12.58 + 2

y = - 2.688975 + 2

y = 0.688975

(x, y) = (3.145, 0.688975)

y = x² - 4x + 2

y = (0.585) ² - 4 (0.585) + 2

y = 0.342225 - 2.34 + 2

y = - 1.997775 + 2

y = 1.997775

(x, y) = (0.585, 1.997775)

Axis of Symmetry

x = 2.56

y = - 1.3088

(x, y) = (2.56, - 1.308)