Question

Graph f(x)=x2 +2x-3 label x and y intercept and vertex with their coordinates and draw axis of symmetry

Answer 1

See below

Step-by-step explanation

The given function is

`f(x)= {x}^(2) + 2x - 3`

We complete the square to rewrite this function in the vertex form.

`f(x)= {x}^(2) + 2x + 1 - 1- 3`

`f(x)= {(x + 1)}^(2) - 4`

The vertex is (-1,-4).

The axis of symmetry is x=-1

To find x-intercepts , put f(x)=0.

`{(x + 1)}^(2) = 4`

`x + 1 = \pm √(4)`

`x = - 1\pm2`

`x = - 3 \: or \: x = 1`

The x-intercepts are (-3,0), (1,0)

To find y-intercept , put x=0.

`f(x)= {0}^(2) + 2(0) - 3 = - 3`

The graph is shown in the attachment.