Question

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Answer 1

The axis of symmetry is x = 1

The vertex of the parabola 2x² - 4x is (1, -2)

Explanation:

`f(x) = 2 {x}^(2) - 4x`

first find the axis of symmetry

`x = - (b)/(2a) = - ( - 4)/(2(2)) = - ( - 4)/(4) = (4)/(4) = 1`

Now substitute this value back into the original equation and solve for f(x) = y

`y = 2 ({1}^(2) ) - 4(1) \\ y = 2 - 4 = - 2`

The vertex of the parabola is

`(x \: \: \: y) = (1 \: \: \: - 2)`

NOTE: separate the XY pair with a comma so

(x,y) = (1, -2)