Question

Name:

6. Graph the following function in factored form and identify all key features

f(x) = 2(x - 1)(x + 3)
Zeros:
Axis of symmetry: x =
Vertex:
Y-Intercept:

Answer 1

See below

Explanation:

Zeroes

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

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

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

`x=1` and
`x=-3`

`(1,0)` and
`(-3,0)`

Axis of Symmetry

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

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

`y=2(x^2+2x-3)`

`y+2(4)=2(x^2+2x-3+4)`

`y+8=2(x^2+2x+1)`

`y+8=2(x+1)^2`

`y=2(x+1)^2-8`

`y=a(x-h)^2+k`

`x=h`

`x=-1`

Vertex

`y=a(x-h)^2+k`

`y=2(x+1)^2-8`

`(h,k)\rightarrow(-1,-8)`

Y-intercept

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

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

`f(0)=2(-1)(3)`

`f(0)=-6`

`y=-6`

`(0,-6)`

Please review the attached graph for a visual of these key features.