Question

What is the axis of symmetry and vertex for the graph `y= -7x^2 +2x`?

Answer 1

`x=1/7," vertex "=(1/7,1/7)`

Explanation:

`"calculate the zeros by letting y = 0"`

`-7x^2+2x=0`

`x(-7x+2)=0`

`x=0,x=2/7larrcolor(blue)"are the zeros"`

`"the vertex lies on the axis of symmetry which is"`
`"situated at the midpoint of the zeros"`

`"axis of symmetry "x=(0+2/7)/2=1/7`

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

`y=-7(1/7)^2+2(1/7)=-1/7+2/7=1/7`

`color(magenta)"vertex "=(1/7,1/7)`
graph{-7x^2+2x [-10, 10, -5, 5]}