Axis of Symmetry for a Parabola
The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves.
The axis of symmetry always passes through the vertex of the parabola.
So we only need to find the x-coordinate of the vertex of the parabola.
A parabola is the graph of a quadratic function as follows:
[tex]y=ax^2+bx+c[/tex]The x-coordinate of the vertex is given by:
[tex]x_v=-\frac{b}{2a}[/tex]We are given the function:
[tex]y=x^2-5x[/tex]Here we have the values: a = 1, b = -5, c = 0.
Calculating:
[tex]\begin{gathered} x_v=-\frac{-5}{2(1)} \\ x_v=\frac{5}{2} \end{gathered}[/tex]Thus, the axis of symmetry of the parabola is x = 5/2