ANSWER
See below
EXPLANATION
The given function is
[tex]f(x)= {x}^{2} + 2x - 3[/tex]
We complete the square to rewrite this function in the vertex form.
[tex]f(x)= {x}^{2} + 2x + 1 - 1- 3[/tex]
[tex]f(x)= {(x + 1)}^{2} - 4[/tex]
The vertex is (-1,-4).
The axis of symmetry is x=-1
To find x-intercepts , put f(x)=0.
[tex]{(x + 1)}^{2} = 4[/tex]
[tex]x + 1 = \pm \sqrt{4} [/tex]
[tex]x = - 1\pm2[/tex]
[tex]x = - 3 \: or \: x = 1[/tex]
The x-intercepts are (-3,0), (1,0)
To find y-intercept , put x=0.
[tex]f(x)= {0}^{2} + 2(0) - 3 = - 3[/tex]
The graph is shown in the attachment.
