Question

Determine the axis of symmetry and the vertex of the given function. y = 2x2 − 12x + 21 Axis of symmetry:

Answer 1

Equation of the axis of symmetry is: x = 3

Explanation:

The equation

`y=2x^2-12x+21`

is the equation of a parabola, of the form

`y=ax^2+bx+c` whose vertex is located at the x-coordinate:

`x_(vertex)=(-b)/(2\,a)`

Then, for our case the x position of the given parabola, is:

`x_(vertex)=(-b)/(2\,a) \\x_(vertex)=(12)/(2\,(2)) \\x_(vertex)=3`

Then the equation of the axis of symmetry, which is a vertical line that goes through the vertex, would be given by:

x = 3