Answer:
[tex]x_1=3.55[/tex]
[tex]x_2=-1.55[/tex]
Step-by-step explanation:
we know that
If the vertex is (1,-13) and the y-intercept is (0.-11) (y-intercept above the vertex), we have a vertical parabola open upward
The equation of a vertical parabola written in vertex form is equal to
[tex]y=a(x-h)^2+k[/tex]
where
a is a coefficient
(h,k) is the vertex
substitute the given value of the vertex
[tex]y=a(x-1)^2-13[/tex]
Find the value of a
Remember that we have the y-intercept
For x=0, y=-11
substitute
[tex]-11=a(0-1)^2-13[/tex]
[tex]a=13-11\\a=2[/tex]
so
[tex]y=2(x-1)^2-13[/tex]
Find the x-intercepts
For y=0
[tex]2(x-1)^2-13=0[/tex]
[tex]2(x-1)^2=13[/tex]
[tex](x-1)^2=6.5[/tex]
[tex]x-1=\pm\sqrt{6.5}[/tex]
[tex]x=1\pm\sqrt{6.5}[/tex]
[tex]x_1=1+\sqrt{6.5}=3.55[/tex]
[tex]x_2=1-\sqrt{6.5}=-1.55[/tex]
