Question

finding intercepts of quadratic functions
consider the function ( f(x) = x^2 + 12x + 11 ).
( x )-intercepts:
( 0 = x^2 + 12x + 11 )
( 0 = (x + 1)(x + 11) )
( y )-intercept:
( f(0) = (0)^2 + 12(0) + 11 )
what are the intercepts of the function?
the ( x )-intercepts are
the ( y )-intercept is
options for ( x )-intercepts: ((-1, 0)) and ((-11, 0)); ((0, -1)) and ((0, -11)); ((0, 1)) and ((0, 11)); ((1, 0)) and ((11, 0))

Explanation:

Step1: Solve for x-intercepts

Set $f(x)=0$, so $x^2 + 12x + 11 = 0$. Factor to get $(x+1)(x+11)=0$. Solve: $x+1=0 \implies x=-1$; $x+11=0 \implies x=-11$. Thus x-intercepts are $(-1,0)$ and $(-11,0)$.

Step2: Solve for y-intercept

Set $x=0$, calculate $f(0)=(0)^2 + 12(0) + 11 = 11$. Thus y-intercept is $(0,11)$.

Answer:

The x-intercepts are $(-1, 0)$ and $(-11, 0)$
The y-intercept is $(0, 11)$