Question

What is the axis of symmetry and vertex for the graph `y = 2x^2 - 4x + 1`?

Answer 1

The axis of symmetry is the line `x = 1`, and the vertex is the point (1, -1).

Explanation:

The standard form of a quadratic function is `y = ax^2 + bx + c`. The formula for finding the equation of the axis of symmetry is `x = (-b)/(2a)`. The x-coordinate of the vertex is also `(-b)/(2a)`, and the y-coordinate of the vertex is given by substituting the x-coordinate of the vertex into the original function.

For `y = 2x^2 - 4x +1`, `a = 2`, `b = -4`, and `c = 1`.

The axis of symmetry is:
`x = (-1*-4)/(2*2)`
`x = 4/4`
`x = 1`

The x-coordinate of the vertex is also 1. The y-coordinate of the vertex is found by:
`y = 2(1)^2 - 4(1) + 1`
`y = 2(1) - 4 + 1`
`y = 2 -3`
`y = -1`
So, the vertex is the point (1, -1).