Answer:
x-intercepts are
[tex]x=1[/tex]
[tex]x=3[/tex]
Step-by-step explanation:
we are given equation as
[tex]y=-3x^2+12x-9[/tex]
For finding x-intercept , we can set y=0
and then we can solve for x
[tex]y=-3x^2+12x-9=0[/tex]
we can factor it
[tex]-3(x^2-4x+3)=0[/tex]
[tex]-3(x-1)(x-3)=0[/tex]
now, we can set each terms to 0
and then we can solve for x
[tex](x-1)=0[/tex]
[tex]x=1[/tex]
[tex](x-3)=0[/tex]
[tex]x=3[/tex]
So, x-intercepts are
[tex]x=1[/tex]
[tex]x=3[/tex]
