Question

How do you find the axis of symmetry, and the maximum or minimum value of the function `y=x^2-5x+3`?

Answer 1

Axis of symmetry is parallel to y-axis, x = `3/2`.
Minimum y = `-13/4`.
y increases from `-13/4` without limit.

Explanation:

`(x-5/2)^2=y-13/4`.
This represents the parabola with vertex at `(5/2, -13/4)`, with axis of symmetry parallel to y-axis x = 3/2.
`dy/dx = 2 x-5 = 0 to x = 5/2`.
`(d^2y)/(dx^2)= 2 > 0 to` y is min, when x=5/2.
There is no maximum.