Question

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`?

Answer 1

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

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