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

Answer:

See below

Step-by-step 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.