# How do you find the y intercept, the equation of the axis of symmetry and the x-coodinate of the vertex f(x)= x^2 - 10x + 5?

Apr 22, 2015

y-intercept is 5, Axis of symmetry is x=5, x-coordinate of vertex is 5.

To find the axis of symmetry, and the coordinates of the vertex, this quadratic function need be put in its standard form (parabola):

y= ${x}^{2} - 10 x + 5$
= ${x}^{2} - 10 x + 25 - 25 + 5$
= ${\left(x - 5\right)}^{2} - 20$
y+20= ${\left(x - 5\right)}^{2}$
Compare this with the standard form of a vertical parabola y-k =${\left(x - h\right)}^{2}$ with vertex (h,k) and axis of symmetry x=h

The vertex is therefore (5, -20) and axis of symmetry is x=5