Question

What is the axis of symmetry and vertex for the graph `y=x^2-8x+3`?

Answer 1

`color(blue)("Vertex"->(x,y)->(4,-13)`
`color(blue)("Axis of symmetry"->x=4)`

Explanation:

Standard form:`" "y=ax^2+bx+c`

Write as:`" "y=a(x^2+b/a x)+c`

With a quadratic, the axis of symmetry passes through `x_("vertex")`

In the case of this question `a=1`

`color(blue)(x_("vertex")=(-1/2)xxb/a " "-> (-1/2)xx(-8)=+4)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
By substitution:

`color(blue)(y_("vertex")=(4)^2-8(4)+3 =-13)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Vertex"->(x,y)->(4,-13)`
`color(blue)("Axis of symmetry"->x=4)`