Question

What is the vertex, axis of symmetry, of `y=4-8x^2+3x`? Does the parabola open up or down?

Answer 1

`"see explanation"`

Explanation:

`"for a parabola in standard form " y=ax^2+bx+c`

`• " if " a>0" then parabola opens up " uuu`

`• " if " a<0" then parabola opens down " nnn`

`y=-8x^2+3x+4" is in standard form"`

`"with " a=-8,b=3,c=4`

`"since " a<0" parabola opens down"`

`"the x-coordinate of the vertex " x_(color(red)"vertex")=-b/(2a)`

`rArrx_(color(red)"vertex")=-3/(-16)=3/16`

`"substitute into equation for y-coordinate of vertex"`

`y_(color(red)"vertex")=-8(3/16)^2+3(3/16)+4=137/32`

`rArrcolor(magenta)"vertex " =(3/16,137/32)`

`"the axis of symmetry passes through the vertex, is a vertical"`
`"line with equation"`

`x=3/16`
graph{(y+8x^2-3x-4)(y-1000x+375/2)=0 [-10, 10, -5, 5]}