Find the line of symmetry for the parabola whose equation is y = 2x² - 4x + 1.

Solution:

The line of symmetry is a line that divides an object into two identical pieces. Here, we have a star and we can fold it into two equal halves.

When a figure is folded in half, along its line of symmetry, both the halves match each other exactly.

This line of symmetry is called the axis of symmetry.

Given: Equation is y = 2x² - 4x + 1.

Differentiate with respect to x, we get

dy/dx = 4x - 4

The line of symmetry is present where the curve turns

It is when the gradient of the curve is zero

dy/dx = 0

4x - 4 = 0

Now solve for x,

4x = 4

x = 1

Therefore, the line of symmetry for the parabola is x = 1.

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Find the line of symmetry for the parabola whose equation is y = 2x² - 4x + 1.

Summary:

The line of symmetry for the parabola whose equation is y = 2x² - 4x + 1 is x = 1.