Question

How do you find the vertex and intercepts for `y=2(x+1)(x-3)`?

Answer 1

`(1,-8),x=-1,x=3`

Explanation:

`"to find the intercepts set y = 0"`

`2(x+1)(x-3)=0`

`x+1=0rArrx=-1`

`x-3=0rArrx=3`

`"the vertex is on the axis of symmetry which is positioned"`
`"at the midpoint of the x-intercepts"`

`x_("vertex")=(-1+3)/2=1`

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

`y_("vertex")=2(2)(-2)=-8`

`color(magenta)"vertex "=(1,-8)`

`"for y-intercept set x = 0"`

`y=2(1)(-3)=-6`
graph{2(x+1)(x-3) [-16.02, 16.02, -8.01, 8.01]}