Question

What is the axis of symmetry and vertex for the graph `y= -2x^2+12x -10`?

Answer 1

Axis of Symmetry `-> x=3`
`y_("vertex")=-2(3)^2+12(3)-10 =-8`
`x_("vertex")=x_("AxisSym")= 3`

Explanation:

Given:`" "y=-2x^2+12x-10`

Write as:`" "y=-2(x^2-color(red)(6)x)-10`

Consider `color(red)(-6)" from "-6x`

`x_("AxisSym")=(-1/2)xxcolor(red)((-6))=+3`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`y_("vertex")=-2(3)^2+12(3)-10 =-8`
`x_("vertex")=x_("AxisSym")= 3`