Answer
x-intercepts= (-3,0) and (4,0)
y-intercept= (0,-12)
minimum= (0.5 , -12.25)
Explanation
Factoring we get:
[tex]x^2-x-12=(x+3)(x-4)[/tex]
For y-intercepts (y=0):
[tex]\begin{gathered} x+3=0 \\ x=-3 \end{gathered}[/tex]
and
[tex]\begin{gathered} x-4=0 \\ x=4 \end{gathered}[/tex]
for x-intercepts (x=0):
[tex]\begin{gathered} f(0)=0^2-0-12 \\ f(^0)=-12 \end{gathered}[/tex]
the minimum must be at the value of x in the middle of -3 and 4, this is 0.5, and replacing:
[tex]\begin{gathered} f(0.5)=0.5^2-0.5-12 \\ f(0.5)=0.25-0.5-12 \\ f(0.5)=-12.25 \end{gathered}[/tex]
