Question

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

Answer 1

Answer:

Equation of the axis of symmetry is:   x = 3

Step-by-step 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:

$x_{vertex}=\frac{-b}{2\,a}$

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

$x_{vertex}=\frac{-b}{2\,a} \\x_{vertex}=\frac{12}{2\,(2)} \\x_{vertex}=3$

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

x = 3