Question

What is the axis of symmetry and vertex for the graph `y=8(x-3)^2+5`?

Answer 1

`"vertex "=(3,5)`
`"axis of symmetry is " x=3`

Explanation:

The equation of a parabola in `color(blue)"vertex form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))`
where (h ,k) are the coordinates of the vertex and a is a constant.

`y=8(x-3)^2+5" is in this form"`

`"with " h=3" and " k=5`

`rArrcolor(magenta)"vertex "=(3,5)`

The parabola is symmetrical about the vertex and the axis of symmetry passes through the vertex, vertically.

graph{(y-8x^2+48x-77)(y-1000x+3000)=0 [-16.02, 16.02, -8.01, 8.01]}
`rArrcolor(magenta)"axis of symmetry has equation " x=3`