Question

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

Answer 1

`"vertex "=(0,-12)," intercepts "x=+-2`

Explanation:

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

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

`"equate each factor to zero and solve for x"`

`x-2=0rArrx=2`

`x+2=0rArrx=-2`

`"to find the y-intercept set x = 0"`

`y=3(-2)(+2)=-12`

`"The vertex lies on the line of symmetry which is"`
`"positioned midway between the x-intercepts"`

`x_("vertex")=(+2-2)/2=0`

`y_("vertex")=3(-2)(+2)=-12`

`color(magenta)"vertex "=(0,-12)`
graph{3(x-2)(x+2) [-40, 40, -20, 20]}