Question

What is the axis of symmetry and vertex for the graph `y= -2x^2 + 24x - 10`?

Answer 1

`x=6,(6,62)`

Explanation:

`"given the equation of a parabola in standard form"`

`•color(white)(x)ax^2+bx+c color(white)(x);a!=0`

`"the x-coordinate of the vertex and the axis of symmetry is"`

`x_(color(red)"vertex")=-b/(2a)`

`y=-2x^2+24x-10" is in standard form"`

`"with "a=-2,b=24,c=-10`

`rArrx_(color(red)"vertex")=-24/(-4)=6`

`"substitute this value into the equation for the"`
`"corresponding y-coordinate"`

`rArry_(color(red)"vertex")=-72+144-10=62`

`rArrcolor(magenta)"vertex "=(6,62)`

`"equation of axis of symmetry is "x=6`
graph{(y+2x^2-24x+10)(y-1000x+6000)=0 [-160, 160, -80, 80]}