The axis of symmetry is a vertical line that goes through the lowest point of the parabola, which is exactly in the middle between the roots. So, find the roots and the point that is the exact middle between them, that would be the position of the vertical axis of symmetry.
The other tutor (@wynona) provided good instructions.
I will show another (shorter) way to avoid using the quadratic formula.
y = .
Notice that the right-hand side function has a very convenient form to complete the square
= - = .
The minimum of the function is achieved at x = -1/3; hence, x = -1/3 is the symmetry axis.
There is an even shorter way to find the symmetry axis for any quadratic function y = .
Use the formula = . (1)
This formula is a direct consequence of the procedure of completing the square.
It is also a direct consequence of the quadratic formula.
When you solve such a problem for the first time, or the first three times, you can use either the quadratic formula
or completing the square.
But if you solve such problems ten times or 15 times, as you are usually assigned in school, then using formula (1)
becomes much more preferable.
Solved with extended instructions.
Tutor's @wynona solutions were very instructive on this forum.
I regret that she stopped her activity on this forum after 4 (four) of her posts.
Potentially, she could be a very successful tutor, because her thinking and writing are very rational.
