Answer:
The graph in the attached figure
Step-by-step explanation:
we know that
The equation of a vertical parabola in vertex form is equal to
[tex]y=a(x-h)^{2}+k[/tex]
where
a is a coefficient
(h,k) is the vertex
In this problem we have
(h,k)=(1,-4)
substitute
[tex]y=a(x-1)^{2}-4[/tex]
we have
An x-intercept of (-1,0)
substitute and solve for a
[tex]0=a(-1-1)^{2}-4[/tex]
[tex]0=4a-4[/tex]
[tex]4a=4[/tex]
[tex]a=1[/tex]
The equation is
[tex]y=(x-1)^{2}-4[/tex]
Verify the y-intercept
For x=0
[tex]y=(0-1)^{2}-4[/tex]
[tex]y=-3[/tex]
The y-intercept is the point (0,-3) -----> is correct
using a graphing tool
see the attached figure
