The axis of symmetry of a parabola is a line that divides it into two similar halves and this axis always goes through the vertex.
To find the equation of the line that represents the symmetry of the curve, suppose a parabola of the form [tex]y = ax ^ 2 + bx + c[/tex]
Then, deriving y with respect to x we have:
[tex]\frac{dy}{dx} = 2ax + b[/tex]
By matching dy / dx to 0 we have and by clearing x we have:
[tex]x = \frac{-b}{2a}[/tex]
This equation allows us to find the axis of symmetry for any quadratic function
Then for the first function of the image.
The axis of symmetry is:
[tex]x = \frac{16}{2*2}[/tex]
[tex]x = 4[/tex]
For the second function of the image:
[tex]x =\frac{-(-10)}{2*5}[/tex]
[tex]x = 1[/tex]
For the third function the axis of symmetry is observed with the naked eye, is the line of equation:
[tex]x = -2[/tex]
